Edexcel GCSE Maths - Probability of Events (FH)

1. Four teams, City, Rovers, Town and United play a competition to win a cup. Only one team can
win the cup.

The table below shows the probabilities of City or Rovers or Town winning the cup.

City Rovers Town United

0.38 0.27 0.15 x

Work out the value of x.

.........................
(Total 2 marks)

2. The table shows information about the number of fillings the students in a class had last year.

Number of Number of
fillings students
0 10
1 5
2 4
3 2
More than 3 1

The headteacher is to choose a student at random from the class.

Find the probability that she will choose a student who had

(a) exactly 1 filling,

…………………
(1)
Edexcel GCSE Maths - Probability of Events (FH)

(b) 2 or more fillings,

…………………
(1)

(c) either 1 filling or 2 fillings.

…………………
(1)
(Total 3 marks)

3. The probability that a biased dice will land on a four is 0.2

Pam is going to roll the dice 200 times.

Work out an estimate for the number of times the dice will land on a four.

.........................
(Total 2 marks)

4. The probability that a biased dice will land on a four is 0.2

Pam is going to roll the dice 200 times.

Work out an estimate for the number of times the dice will land on a four.

.........................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

5. Mr Brown chooses one book from the library each week.

He chooses a crime novel or a horror story or a non-fiction book.

The probability that he chooses a horror story is 0.4

The probability that he chooses a non-fiction book is 0.15

Work out the probability that Mr Brown chooses a crime novel.

…………………….
(Total 2 marks)

6. Here is a 4-sided spinner.

The sides of the spinner are labelled 1, 2, 3 and 4.

The spinner is biased.
The probability that the spinner will land on each of the numbers 2 and 3 is given in the table.
The probability that the spinner will land on 1 is equal to the probability that it will land on 4.

Number 1 2 3 4
Probability x 0.3 0.2 x

(a) Work out the value of x.

x = ………………….
(2)
Edexcel GCSE Maths - Probability of Events (FH)

Sarah is going to spin the spinner 200 times.

(b) Work out an estimate for the number of times it will land on 2

…………………….
(2)
(Total 4 marks)

7. A school snack bar offers a choice of four snacks.

The four snacks are burgers, pizza, pasta and salad.
Students can choose one of these four snacks.

The table shows the probability that a student will choose burger or pizza or salad.

Snack burger pizza pasta salad

Probability 0.35 0.15 0.2

One student is chosen at random from the students who use the snack bar.

(a) Work out the probability that the student

(i) did not choose salad,

.................................

(ii) chose pasta.

.................................
(3)
Edexcel GCSE Maths - Probability of Events (FH)

300 students used the snack bar on Tuesday.

(b) Work out an estimate for the number of students who chose pizza.

.................................
(2)
(Total 5 marks)

8. A school snack bar offers a choice of four snacks.

The four snacks are burgers, pizza, pasta and salad.
Students can choose one of these four snacks.

The table shows the probability that a student will choose burger or pizza or salad.

Snack burger pizza pasta salad

Probability 0.35 0.15 0.2

300 students used the snack bar on Tuesday.

Work out an estimate for the number of students who chose pizza.

.................................
(Total 2 marks)

9. Fred did a survey of the time, in seconds, people spent in a queue at a supermarket.
Information about the times is shown in the table.

Time (t seconds) Frequency

0 < t ≤ 40 8
40 < t ≤ 80 12
80 < t ≤ 120 14
120 < t ≤ 160 16
160 < t ≤ 200 10
Edexcel GCSE Maths - Probability of Events (FH)

(a) Write down the modal class interval.

………………………seconds
(1)

A person is selected at random from the people in Fred’s survey.

(b) Work out an estimate for the probability that the person selected spent more than
120 seconds in the queue.

………………………
(2)
(Total 3 marks)

10. Fred did a survey of the time, in seconds, people spent in a queue at a supermarket.
Information about the times is shown in the table.

Time(t seconds) Frequency

0 < t ≤40 8
40 < t ≤ 80 12
80 < t ≤ 120 14
120 < t ≤ 160 16
160 < t ≤ 200 10

A person is selected at random from the people in Fred’s survey.

Work out an estimate for the probability that the person selected spent more than
120 seconds in the queue.

………………………
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

11. 70 students each chose one P.E. activity.

They chose one of basketball or swimming or football.
The two-way table shows some information about their choices.

Basketball Swimming Football Total

Female 10 37
Male 17
Total 19 22 70

(a) Complete the two-way table.

(3)

One of these students is picked at random.

(b) Write down the probability that this student chose basketball.

.........................................
(2)
(Total 5 marks)

12. Mr Brown buys a garden spade.

The spade costs £20 plus 17½% VAT.

Garden spade
£20 + 17½ % VAT
Edexcel GCSE Maths - Probability of Events (FH)

(a) Calculate the total cost of the spade.

£ .......................................
(3)

Mr Brown makes some compost.

He mixes soil, manure and leaf mould in the ratio 3:1:1

Mr Brown makes 75 litres of compost.

(b) How many litres of soil does he use?

................................ litres
(3)
Edexcel GCSE Maths - Probability of Events (FH)

Mr Brown sows 200 flower seeds.

For each flower seed the probability that it will produce a flower is 0.8

(c) Work out an estimate for the number of these flower seeds that will produce a flower.

.........................................
(2)
(Total 8 marks)

13. Mr Brown makes some compost.

He mixes soil, manure and leaf mould in the ratio 3:1:1

Mr Brown makes 75 litres of compost.

(a) How many litres of soil does he use?

................................. litres
(3)
Edexcel GCSE Maths - Probability of Events (FH)

Mr Brown sows 200 flower seeds.

For each flower seed the probability that it will produce a flower is 0.8

(b) Work out an estimate for the number of these flower seeds that will produce a flower.

..........................................
(2)
(Total 5 marks)

14. A DIY store bought 1750 boxes of nails.

Barry took 25 of these boxes and counted the number of nails in each.
The table shows his results.

Number of nails Number of boxes

14 2
15 9
16 8
17 4
18 2

The numbers of nails in the 25 boxes are typical of the numbers of nails in the 1750 boxes.

Work out an estimate for how many of the 1750 boxes contain 16 nails.

......................................
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (FH)

15. A bag contains counters which are red or green or yellow or blue.

The table shows each of the probabilities that a counter taken at random from the bag will be red
or green or blue.

Colour Red Green Yellow Blue

Probability 0.2 0.3 0.1

A counter is to be taken at random from the bag.

(a) Work out the probability that the counter will be yellow.

.....................................
(2)

The bag contains 200 counters.

(b) Work out the number of red counters in the bag.

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (FH)

16. The two-way table shows some information about the colours of Ford cars and of Toyota cars in
a garage.

white blue red Total

Ford 5 21
Toyota 7
Total 9 16 40

(a) Write down the total number of white cars.

.....................................
(1)

(b) Complete the two-way table.

(3)

(c) One of these 40 cars is to be picked at random.

Work out the probability that this car will be blue.

.....................................
(1)
(Total 5 marks)

17. Joe rolls a 6-sided dice and spins a 4-sided spinner.

The dice is labelled 1, 2, 3, 4, 5, 6

The spinner is labelled 1, 2, 3, 4

4
3

4
2
1
Edexcel GCSE Maths - Probability of Events (FH)

Joe adds the score on the dice and the score on the spinner to get the total score.

He records the possible total scores in a table.

+ 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3
3 4
4 5

(a) Complete the table of possible total scores.

(2)

(b) Write down all the ways in which Joe can get a total score of 5
One of them has been done for you.

(1, 4), .....................................

(2)

(c) Write down all the ways Joe can get a total score of 8 or more.

…………………......................................
(2)
(Total 6 marks)
Edexcel GCSE Maths - Probability of Events (FH)

18. Here are the ages, in years, of 15 teachers.

35 52 42 27 36

23 31 41 50 34

44 28 45 45 53

(a) Draw an ordered stem and leaf diagram to show this information.
You must include a key.

Key:

(3)

One of these teachers is picked at random.

(b) Work out the probability that this teacher is more than 40 years old.

....................................
(2)
(Total 5 marks)
Edexcel GCSE Maths - Probability of Events (FH)

19. There are 3 red pens, 4 blue pens and 5 black pens in a box.
Sameena takes a pen, at random, from the box.

Write down the probability that she takes a black pen.

.........................
(Total 2 marks)

20. Here is a 4-sided spinner.

Red
Blue

Yellow
Green

The sides of the spinner are labelled Red, Blue, Green and Yellow.
The spinner is biased.
The table shows the probability that the spinner will land on each of the colours Red, Yellow
and Green.

Colour Red Blue Green Yellow

Probability 0.2 0.3 0.1

Work out the probability the spinner will land on Blue.

....................................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

21. There are 3 red pens, 4 blue pens and 5 black pens in a box.
Sameena takes a pen, at random, from the box.

(a) Write down the probability that she takes a black pen.

........................
(2)

(b) Write down the probability that Sameena takes a pen that is not black.

........................
(1)
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (FH)

22. Here is a 5-sided spinner.

The sides of the spinner are labelled 1, 2, 3, 4 and 5

The spinner is biased.
The probability that the spinner will land on each of the numbers 1, 2, 3 and 4 is given in the
table.

Number 1 2 3 4 5
Probability 0.15 0.05 0.2 0.25 x

Work out the value of x.

x = ....................................
(Total 2 marks)

23. The two-way table gives some information about how 100 children travelled to school one day.

Walk Car Other Total

Boy 15 14 54
Girl 8 16
Total 37 100

(a) Complete the two-way table.

(3)
Edexcel GCSE Maths - Probability of Events (FH)

One of the children is picked at random.

(b) Write down the probability that this child walked to school that day.

.....................................
(1)

One of the girls is picked at random.

(c) Work out the probability that this girl did not walk to school that day.

.....................................
(2)
(Total 6 marks)

24. The two-way table gives some information about how 100 children travelled to school one day.

Walk Car Other Total

Boy 15 14 54
Girl 8 16
Total 37 100

(a) Complete the two-way table.

(3)

One of the children is picked at random.

(b) Write down the probability that this child walked to school that day.

.....................................
(1)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (FH)

25. A box contains bricks which are orange or blue or brown or yellow.
Duncan is going to choose one brick at random from the box.

The table shows each of the probabilities that Duncan will choose an orange brick or a brown
brick or a yellow brick.

Colour Orange Blue Brown Yellow

Probability 0.35 0.24 0.19

Work out the probability that Duncan will choose a blue brick.

……………………………
(Total 2 marks)

26. The probability that a biased dice will land on a six is 0.4.
Marie is going to throw the dice 400 times.

Work out an estimate for the number of times the dice will land on a six.

……………………………
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

27. Here are the times, in minutes, taken to change some tyres.

5 10 15 12 8 7 20 35 24 15

20 33 15 25 10 8 10 20 16 10

(a) In the space below, draw a stem and leaf diagram to show these times.

(3)

The probability that a new tyre will be faulty is 0.05

(b) Work out the probability that a new tyre will not be faulty.

.............................
(1)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (FH)

28. A train can be on time or early or late.

The probability that the train will be on time is 0.69

The probability that the train will be early is 0.07

Work out the probability that the train will be late.

………………….
(Total 2 marks)

29. Richard has a box of toy cars.

Each car is red or blue or white.

3 of the cars are red.

4 of the cars are blue.
2 of the cars are white.

Richard chooses one car at random from the box.

Write down the probability that Richard will choose a blue car.

……………………
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

30. The probability that a biased dice will land on a three is 0.24
Susan is going to throw the dice 300 times.

Work out an estimate for the number of times the dice will land on a three.

………………..
(Total 2 marks)

31. A box contains sweets which are red or green or yellow or orange.

The probability of taking a sweet of a particular colour at random is shown in the table.

Colour Red Green Yellow Orange

Probability 0.25 0.1 0.3

Sarah is going to take one sweet at random from the box.

Work out the probability that Sarah will take an orange sweet.

..........................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

32. A bag contains some balls which are red or blue or green or black.
Yvonne is going to take one ball at random from the bag.

The table shows each of the probabilities that Yvonne will take a red ball or a blue ball or a
black ball.

Colour Red Blue Green Black

Probability 0.3 0.17 0.24

Work out the probability that Yvonne will take a green ball.

..........................
(Total 2 marks)

33. A bag contains some sweets.

The flavours of the sweets are either strawberry or chocolate or mint or orange.
Sarah is going to take one sweet at random from the bag.

The table shows the probability that Sarah will take a strawberry sweet or a mint sweet or an
orange sweet.

Flavour Strawberry Chocolate Mint Orange

Probability 0.32 0.17 0.2

Work out the probability that Sarah will take a chocolate sweet.

.............................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

34. A bag contains coloured counters.

The counters are either red or green or blue.

Dean takes at random a single counter from the bag.

The probability that he takes a red counter is 0.5

The probability that he takes a green counter is 0.15

(a) What is the probability that he takes a blue counter?

........................................
(2)

A box contains 50 counters.

There are 23 white counters, 19 black counters and 8 yellow counters.

Piero takes at random a single counter from the box.

(b) Work out the probability that he takes a white counter or a yellow counter.

(2)
(Total 4 marks)

35. Each day, Anthony travels to work.

He can be on time or early or late.

The probability that he will be on time is 0.02

The probability that he will be early is 0.79

Work out the probability that Anthony will be late.

......................................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

36. 20 000 adults live in Mathstown.

The probability that one of these adults, chosen at random, will vote in an election is 0.7

Work out an estimate for the number of these adults who will vote in an election.

.....................................
(Total 2 marks)

37. Liam rolls a fair 6-sided dice once.

Write down the probability that the dice will show a 2 or a 3

..........................
(Total 2 marks)

38. Mia spins a spinner.

The spinner can land on red or green or blue or pink.

The table shows each of the probabilities that the spinner will land on red or green or blue.

Colour Red Green Blue Pink

Probability 0.4 0.1 0.2

Work out the probability that the spinner will land on pink.

.....................................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

39. Marco has a 4-sided spinner.

The sides of the spinner are numbered 1, 2, 3 and 4
The spinner is biased.

3
2

1
The table shows the probability that the spinner will land on each of the numbers 1, 2 and 3

Number 1 2 3 4

Probability 0.20 0.35 0.20

Work out the probability that the spinner will land on the number 4

.....................................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

40. There are 8 pencils in a pencil case.

1 pencil is red.
4 pencils are blue.
The rest are black.

A pencil is taken at random from the pencil case.

Write down the probability that the pencil is black.

.....................................
(Total 2 marks)

41. A bag contains counters which are blue or red or green or yellow.
Mark takes a counter at random from the bag.

The table shows the probabilities he takes a blue counter or a red counter or a yellow counter.

Colour blue red green yellow

Probability 0.3 0.2 0.1

(a) Work out the probability that Mark takes a green counter.

..........................
(2)
Edexcel GCSE Maths - Probability of Events (FH)

Mark puts the counter back into the bag.

Laura takes a counter at random from the bag.

She looks at its colour then puts the counter back into the bag.
She does this 50 times.

(b) Work out an estimate for the number of times Laura takes a red counter.

..........................
(2)
(Total 4 marks)

42. A bag contains only red, green and blue counters.

The table shows the probability that a counter chosen at random from the bag will be red or will
be green.

Colour Red Green Blue

Probability 0.5 0.3

Mary takes a counter at random from the bag.

(a) Work out the probability that Mary takes a blue counter.

..........................
(2)
Edexcel GCSE Maths - Probability of Events (FH)

The bag contains 50 counters.

(b) Work out how many green counters there are in the bag.

..........................
(2)
(Total 4 marks)

43. Michael carried out a survey of some students.

He asked them the type of TV programme they liked best.

The accurate pie chart shows some of this information.

Sports

Drama

130° 50°
30°
60° News

Soaps
Comedy

Michael chooses one of the students at random.

Edexcel GCSE Maths - Probability of Events (FH)

(a) (i) Find the probability that this student likes Soaps best.

..............................

(ii) Find the probability that this student does not like Soaps best.

..............................
(2)

6 students said they liked the News best.

(b) How many students took part in the survey?

..............................
(2)
(Total 4 marks)

44. The diagram shows a 3-sided spinner and an ordinary dice.

red
gre 1
blue

en

The spinner has 1 green side, 1 blue side and 1 red side.

Alex spins the spinner once and rolls the dice once.

Write down all the possible outcomes.

One has already been done for you.

(g, 1) ......................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (FH)

45. This coloured wheel spins round.

The sectors are coloured yellow, red, green and blue.

yellow
blue

red
green

Pointer

Diagram NOT accurately drawn

Harry spins the wheel.

When the wheel stops spinning, Harry writes down the colour shown by the pointer.

The probability that the wheel will stop at yellow or red or green is given in the table.

Colour yellow red green blue

Probability 0.35 0.1 0.3

(a) Work out the probability that the wheel will stop at blue.

...........................
(2)

(b) Work out the probability that the wheel will stop at either yellow or red.

...........................
(2)
Edexcel GCSE Maths - Probability of Events (FH)

Hannah is going to spin the wheel 200 times.

(c) Work out an estimate for the number of times the wheel will stop at green.

...........................
(2)
(Total 6 marks)

01. 0.20 2
0.38 + 0.27 + 0.15
M1 1 − sum
A1 cao
[2]

5
02. (a) 1
22
B1 cao

7
(b) 1
22
B1 ft ∑ f used in (a) provided ∑ = 22 ± 2

9
(c) 1
22
B1 ft ∑ f used in (a) provided ∑ = 22 ± 2
[3]

03. 40 2
200 × 0.2
40
M1 for 200 × 0.2 or seen
200
A1 for 40
[2]
Edexcel GCSE Maths - Probability of Events (FH)

04. 40 2
200 × 0.2
40
M1 for 200 × 0.2 or seen
200
A1 for 40
[2]

05. 0.45 2
0.4 + 0.15
1 – “0.55”
M1 for 1 – sum
A1 for 0.45 o.e.
SC B1 for 0.81
[2]

06. (a) 0.25 2

x + 0.3 + 0.2 + x =1
M1 for x + 0.3 + 0.2 + x =1 oe, or 0.5 ÷ 2
A1 oe

(b) 60 2
0.3 × 200
M1 0.3 × 200
A1 cao Accept 60 out of 200 (in words)
60
SC B1 for
200
[4]

07. (a) (i) 1 – 0.2 = 0.8 3

B1 oe

(ii) 1 – (0.35 + 0.15 + 0.2) = 0.3

M1 for 0.35 + 0.15 + 0.2
A1 oe
Edexcel GCSE Maths - Probability of Events (FH)

(b) 0.15 × 300 = 45 2

M1 for 0.15 × 300
A1 cao
45
NB: M1 A0, 45 out of 300 gets M1 A1
300
[5]

08. 0.15 × 300 = 45 2

M1 for 0.15 × 300
A1 cao
[2]

09. (a) 120 < t ≤ 160 1

B1 correct interval eg 120–160

26
(b) 2
60
16
M1 (16 + 10) ÷ ‘60’ or 26 seen or
60
A1 oe
[3]

26
10. 2
60
16
M1 (16 + 10) ÷’60’ or 26 seen or
60
A1 oe
[2]

11. (a) 10 12 15 37 3
9 17 7 33
19 29 22 70
B3 all correct
(B2 for 4 or 5 entries correct)
(B1 for 2 or 3 entries correct)
Edexcel GCSE Maths - Probability of Events (FH)

19
(b) 2
70
19
B2 for , accept 0.27 (....)
70
k
(B1 for with 0 < k < 10 or for the correct probability
70
incorrectly expressed, eg ‘19 out of 70’)
[5]

12. (a) eg 10% + 5% + 2.5% = £2 + £1 + £0.50 3

£20 + £3.50 = 23.50
17.5
M1 for £2, £1 and £0.50 or £3.50 seen or × 20 oe
100
M1 (dep) for “£3.50”+ £20
A1 for 23.5(0)

(b) 75 ÷ (3 + 1 + 1) = 15 3
15 × 3 = 45
M1 for 75 ÷ (3 + 1 + 1)
M1 (dep) for “15” × 3
A1 cao

(c) 0.8 × 200 = 160 2

M1 for 0.8 × 200
A1 for 160, accept 160 out of 200
160
SC: B1 for or 160 in 200
200
[8]

13. (a) 75 ÷ (3 + 1 + 1) = 15 3
15 × 3
= 45
M1 for 75 ÷ (3 + 1 + 1)
M1(dep) for “15” × 3
A1 cao
Edexcel GCSE Maths - Probability of Events (FH)

(b) 0.8 × 200 2

= 160
M1 for 0.8 × 200
A1 for 160, accept 160 out of 200
160
SC: B1 for or 160 in 200
200
[5]

8
14. × 1750 or 0.32 × 1750 or 8 × 70 3
25
= 560
8 1750
M1 for oe seen or oe seen or 0.32 or 70 seen
25 25
8
M1 for × 1750 oe
25
A1 for 560
[3]

15. (a) 1 – (0.2 + 0.3 + 0.1) = 0.4 2

M1 for 1 – (0.2 + 0.3 + 0.1)
0.4
A1 for 0.4 oe, accept
1

(b) 0.2 × 200 = 40 2

M1 for 0.2 × 200
A1 cao
40
NB is M1 A0, 40 out of 200 is M1 A1
200
[4]

16. (a) 9 1
B1 cao
(b) 5 9 7 21 3
4 7 8 19
9 16 15 40
B3 for all correct
(B2 for 4 or 5 correct)
(B1 for 1 or 2 or 3 correct)
Edexcel GCSE Maths - Probability of Events (FH)

16
(c)
40
2
= 1
5
B1 for 2/5 oe
[5]

17. (a) 45678 2

56789
6 7 8 9 10
B2 if fully correct
(B1 for 1 row correct or 2 columns correct)

(b) (1, 4); (2, 3); (3, 2); (4, 1) 2

B2 if fully correct
(B1 for either (2, 3) or (3, 2))

(c) (2, 6); (3, 5); (3, 6); (4, 4); (4, 5); (4, 6) 2
B2 if fully correct (order in brackets need not be consistent)
(B1 for 3 pairs correct, ignore extras)
[6]

18. (a)
2 378
3 1456
4 12455
5 023
2 │ 3 = 23 3
M1 for using 2, 3, 4 and 5 as stem
A1 for ordered stem and leaf diagram
A1 for consistent key, e.g. 2 3 = 23 (years)
OR
M1 for using 20, 30, 40 and 50 as stem
A1 for ordered stem and leaf diagram
A1 for consistent key, e.g. 20│3 = 23 (years)
Edexcel GCSE Maths - Probability of Events (FH)

8
(b) 2
15
'8'
B2 ft for (ft from stem and leaf diagram)
'15'
'8' b
(B1 for , a > ‘8’, or , b < ‘15’)
a '15'
SC: B1 for ‘8’ : ‘15’ or ‘8’ out of ‘15’
[5]

5
19. 2
12
n
M1 for or n ÷ 12 or n ÷ (“3 + 4 + 5”) where n is an
12
integer, where ≤12.
5
A1 or 0.41(6…) or 41.6%
12
[2]

20. 1 – (0.1 + 0.2 + 0.3)

0.4 2
M1 for 1 – (0.1 + 0.2 + 0.3) oe or 0.6 oe seen
A1 for 0.4 oe
[2]

5
21. (a) 2
12
n n
M1 for or n ÷ 12 or or n ÷ (3 + 4 + 5) where n is
12 3+4+5
an integer ≤ 12
5
A1 or 0.41(6…) or 41.6%
12
Edexcel GCSE Maths - Probability of Events (FH)

5
(b) 1–“ ”
12
7
= 1
12
5 7
B1 ft 1 – “ ” provided the answer is positive, or or
12 12
0.58(3…)
[3]

22. 1 – (0.15 + 0.05 + 0.20 + 0.25)

0.35 2
M1 for 1 – (0.15 + 0.05 + 0.20 + 0.25)
A1 for 0.35 oe
[2]

23. (a)
15 25 14 54
22 8 16 46
37 33 30 100

Table 3
B3 for all 5 correct
(B2 for 3 or 4 correct)
(B1 for 1 or 2 correct)

37
(b) 1
100
37
B1 oe
100

24
(c) 2
46
" '46' −'22' "
B2 for oe, ft from no of girls
'46'
(B1 16 + 8 or 24 or ‘46’ seen)
[6]
Edexcel GCSE Maths - Probability of Events (FH)

24. (a)
15 25 14 54
22 8 16 46
37 33 30 100

Table 3
B3 for all 5 correct
(B2 for 3 or 4 correct)
(B1 for 1 or 2 correct)

37
(b) 1
100
37
B1 oe
100
[4]

25. 0.22 oe 2
1 − (0.35 + 0.24 + 0.19)
1 − 0.78
M1 for 1 − (0.35 + 0.24 + 0.19)
A1 cao
[2]

26. 160 2
400 × 0.4
M1 for 400 × 0.4
A1 cao
[2]
Edexcel GCSE Maths - Probability of Events (FH)

27. (a) See working column

05788
1000025556
200045
335
Key 1 3 = 13 (min) 3
B1 for stem 0, 1, 2, 3 or 0, 10, 20, 30
B1 for accurate leaves (in any order) (condone one error or
omission)
B1 for key and ordered leaves all correct
(b) 0.95 1
1 − 0.05
B1 cao
[4]

28. 0.24 oe 2
1 − (0.69 + 0.07)
M1 for 1 − (0.69 + 0.07)
A1
[2]

4
29. 2
9
3+4+2
M1 for denominator of 9 or 4 in 9
or 4 out of 9 (NOT 4 : 9)
A1
[2]

30. 72 2
0.24 × 300
M1 for 0.24 × 300 oe
A1 cao
[2]
Edexcel GCSE Maths - Probability of Events (FH)

31. 0.35oe 2
1 – (0.25 + 0.1 + 0.3)
M1 for 1 – (0.25 + 0.1 + 0.3)
A1 for 0.35 oe
[2]

32. 0.29 2
1 – (0.3 + 0.17 + 0.24)
M1 for 1 – (0.3 + 0.17 + 0.24)
A1 cao
(SC: B1 for 0.56 seen)
[2]

33. 0.31 2
1 − (0.32 + 0.17 + 0.2)
M1 for 1 − (0.32 + 0.17 + 0.2)
A1 for 0.31 oe
S.C. M1A0 for 0.49 or 31
[2]

34. (a) 1 – (0.5 + 0.15)

0.35 oe 2
M1 for 1 – “(0.5 + 0.15)”
A1 for 0.35 oe

31
(b) oe 2
50
23 + 8
M1 for
23 + 8 + 19
31
A1 for or 0.62 oe
50
[sc B1 for 31:50 or 31 to 50]
[4]
Edexcel GCSE Maths - Probability of Events (FH)

35. 1 – (0.02 + 0.79)

0.19 2
M1 for 1 – (0.02+0.79)
A1 cao
[2]

36. 0.7 × 20000

14000 2
M1 for 0.7 × 20000
A1 cao
[2]

1 1 2
37. + = 2
6 6 6
1
= oe
3
1
M1 for oe seen 6
6
or identifying both the 2 and 3 sections in a sample space
diagram of {1, 2, 3, 4, 5, 6}
1
A1 for an answer of oe
3
NOTE: An answer of 2 in 6, 2 out of 6,
2 : 6, oe = M1 A0
[2]

38. 1 – (0.4 + 0.1 + 0.2)

= 1 – 0.7
0.3 2
M1 for 1 – (0.4 + 0.1 + 0.2) or 1 – 0.7
A1 for 0.3 oe
Watch for answer in table.
[2]
Edexcel GCSE Maths - Probability of Events (FH)

39. 1 – (0.2 + 0.35 + 0.2)

0.25 2
M1 for 1 – (0.2 + 0.35 + 0.2)
A1 for 0.25 oe
SC: B1 for “1 out of 4” or “1 in 4”
SC: B1 if 0.25 seen in the table with incorrect answer on
answer line.
[2]

3
40. 2
8
x 3
M1 for (x < 8) or (x > 3)
8 x
3
A1 for o.e.
8
(SC B1 for ‘3 in 8’ or ‘3 out of 8’)
[2]

41. (a) 1 – (0.3 + 0.2 + 0.1)

0.4 2
M1 for 1 – “(0.3 + 0.2 + 0.1)”
A1 for 0.4 oe
(watch out for answers given only in table)

(b) 0.2 × 50
10 2
M1 for 0.2 × 50
A1 for cao
SC B1 for 10/50
[4]

42. (a) 0.2 2

M1 for 1 – ( 0.5 + 0.3)
A1 for 0.2 oe
SC Award M1A0 for an answer of 0.92
Edexcel GCSE Maths - Probability of Events (FH)

(b) 0.3 ×50

15 2
M1 for 0.3 × 50 oe
A1 cao
15
SC Award B1 for on the answer line if M0 scored
50
[4]

90
43. (a) (i) oe 1
360
90
B1 for oe (accept 25% or 0.25 or ¼)
360
Condone any incorrect cancelling if correct answer is seen
Do not accept 1:4 or 4:1 or 1 out of 4 or 3 in 4 etc

270
(ii) oe 1
360
B1 for oe (accept 75% or 0.75 or ¾)
Condone any incorrect cancelling if correct answer is seen
Do not accept 3:4 or 4:3 or 3 out of 4 or 3 in 4 etc
SC: B1 for 1 – (a)(i)
SC: B0 in (i) and B1 in (ii) for correct answers but consistent
writing of probabilities incorrectly in BOTH parts (a)(i) and
(a)(ii) e.g. 1 out of 4 and 3 out of 4

(b) (360 ÷ 30) × 6

72 2
M1 for 360÷30 o.e. e.g.30º is a twelfth or 6÷30 or 30÷6 or 1
person is 5º o.e. or sight of 12×6 or 360 ÷ 5 or attempt add 5
frequencies 3 of which are correct or any partial equivalent
method
A1 cao
[4]

44. (g,1) (g,2) (g,3) (g,4) (g,5) (g,6) (b,1) (b,2)(b,3) (b,4) (b,5) (b,6)
(r,1) (r,2) (r,3) (r,4) (r,5) (r,6) 2
B2 for a fully correct list
[B1 for at least 6 correct additional outcomes]
Ignore duplicates e.g. (g,1) (1, g)
[2]
Edexcel GCSE Maths - Probability of Events (FH)

45. (a) 1 – (0.35 + 0.1 + 0.3)

0.25 2
M1 for 1 – (0.35 + 0.1 + 0.3) oe
A1 for 0.25 oe (accept 25%)
Note:- Look for answer in the table if it’s not on answer line
[SC: B1 for 1 – 0.39 = 0.61, if M0 scored;
0.61 with no working gets no marks]

(b) 0.35 + 0.1

0.45 2
M1 for 0.35 + 0.1 oe
A1 for 0.45 oe
[SC:B1 for an answer of 0.36 or for 0.45 seen in working
followed by subtraction from 1]

(c) 0.3 × 200

60 2
M1 for 0.3 × 200
A1 cao
SC: B2 for 60 out of 200
SC: B1 for 60 in 200 or 60/200 or 0.3 × 200/4
[6]

01. This question was nearly always correct.

02. This question was answered well and many candidates gained full marks. In part (b) some
candidates gave an answer of 4/22, presumably from reading ‘2 or more fillings’ as ‘2 fillings’.

03. This question was answered quite well but it was disappointing that almost one third of those
candidates with a correct method could not work out 200 × 0.2 correctly. This was often
evaluated as 20.

04. Mathematics A Paper 5

In this probability question the method was usually well understood but arithmetical errors were
not uncommon.
Edexcel GCSE Maths - Probability of Events (FH)

Mathematics B Paper 18
The majority of candidates were able to supply correct solutions to this question. Candidates
should be advised to read questions carefully as those who went on to give their answer as a
40
fraction did not gain the final mark as the question asked for ‘the number of times’ that the
200
dice would land on a 4, not the probability. Having identified the correct calculation of 200 ×
0.2, a few candidates were unable to carry this out correctly.

05. Specification A
Foundation Tier
Correct answers were only given by 13% of candidates. A further 12% of candidates gained one
mark. The incorrect response 0.81 suggested some candidates did not have access to or had not
used a calculator to answer this question. The incorrect answer 0.55 was also often seen.
Intermediate Tier
This question was answered well with almost three quarters of candidates gaining full marks. A
significant number, though, wrote 0.4 + 0.15 = 0.19 and gave a final answer of 0.81. A few
added 0.4 and 0.15 but did not subtract the result from 1.

Specification B
There were many correct answers to this question, though 0.81 (1 – 0.19) was the most common
error. Pleasingly only a very few worked in percentages, however of those that did many
showed 55 or 45 without a percentage sign. A significant number of errors were a result of poor
arithmetic.

06. Specification A
Higher Tier
Part (a) was answered well by nearly all the candidates. There were few solutions using algebra-
most candidates simply wrote the answer. A small number thought that 0.5 ÷ 2 was 2.5.
Part (b) was also done well. Some candidates thought that multiplying 200 by 0.3 was the same
as dividing 200 by 3. Some chose to multiply by 0.2 instead of 0.3.
Intermediate Tier
This question was quite well answered by the majority of candidates. In part (a) sometimes the
candidate failed to divide by 2, giving the answer as 0.5, but most gave the correct answer.
There were some errors caused by an inability to divide 0.5 by 2, evidenced by answers such as
0.2.5 or 0.2½. In part (b) the majority of candidates recognised they needed to perform the
calculation 0.3 × 200, and most did so correctly, though a minority could not perform this
calculation without a calculator.
Edexcel GCSE Maths - Probability of Events (FH)

Specification B
Higher Tier
Part (a) was almost always answered correctly. Occasionally candidates forgot to divide by 2
and left the answer as 0.5 or were careless in division and evaluated 0.5 ÷ 2 as 2.5. In part (b),
over 80% of candidates scored full marks. There were, however, a significant number of
1
candidates who used as the fraction equivalent of 0.3 and therefore failed to gain any credit.
3
60
Candidates who gave the final answer as lost the available accuracy mark.
200
Intermediate Tier
Part (a) was well answered with most candidates gaining at least one mark. 0.2 (from
0.3 + 0.2 = 0.6) was a common mistake. A small number of candidates made arithmetic errors
such as 0.5 ÷ 2 = 2.5
In part (b) the usual error was to divide 200 by 0.3 instead of multiplying.

07. Part (a) was well answered, but in the second part many candidates incorrectly added 0.15 +
0.35 + 0.2 = 0.52. In part (b) many candidates knew that they had to calculate 0.15 × 300, but
were unable to do so correctly.

08. This was a relatively straightforward question. There were a few candidates would could not
calculate 300 × 0.15. Some candidates were attracted by the gap and thought that they had to
work out 300 × 0.3.

09. Specification A
Surprisingly only about 1/3 of candidates answered part (a) correctly. Many demonstrated their
confusion with the median (or mean) by choosing the interval from 80. Some chose the correct
interval but then spoilt their answer by giving the midpoint or the frequency as their answer.
Part (b) was well answered. Most used fractions and there were few cases of incorrect notation.
The most common errors included incorrect totalling of the frequencies, picking out the 16 only
16
(to give ) or stating the 26, but not as a probability.
60
Edexcel GCSE Maths - Probability of Events (FH)

Specification B
Part (a) was not answered well, many candidates showing a clear misunderstanding of the
requirements of the question, often giving values 120, 140 or 160 only as their answer. In part
16
(b) most candidates gained at least 1 mark and usually 2. Common wrong answers were or
60
26
; these gained one mark only.
50

10. This question was done well by many candidates. Most appreciated the need to add the
frequencies for both intervals to gain at least one mark for 26. The most common incorrect
16 26 1 34 16 26
answers were and ; and, less commonly, , , and × .
60 50 26 60 60 50

11. This question was answered well. In part (a), more than 80% of candidates completed the two-
way table correctly and almost three quarters of candidates gave the correct probability in part
(b).

12. About half of the candidates calculated the total cost correctly in part (a). Those who were
successful in finding 17½% of £20 had usually calculated 10%, 5% and 2½%. Those who tried
to use 1% and ½% often made errors. Some failed to add on the VAT. A similar proportion of
candidates answered part (b) correctly. A common error was to divide 75 by 3. Some who did
divide by 5 then forgot to multiply by 3 and gave 15 as the final answer. In part (c), 50% of
candidates appreciated the need to multiply 0.8 by 200 but many could not complete the
calculation correctly.

13. This question was done very well. In part (a), most candidates were able to obtain the correct
answer. If an error was made it was usually from dividing 75 by 3 (the compost component of
the ratio) instead of 5. A small number of candidates worked out 3 + 1 + 1 as 4 or 6. In part (b),
some candidates were unable to cope with the multiplication 0.8 × 200, ending up with an
incorrect number of zeros in their answer, typically 1600 or 16.0. A few candidates give their
160
final answer as , thus scoring only one of the two marks available.
200
Edexcel GCSE Maths - Probability of Events (FH)

14. Paper 5524

Candidates were sometimes confused as to how to approach this question. Those who realised it
was a probability question usually moved on to obtain the correct answer, whilst those who
thought it was a frequency distribution did not. Others stopped after dividing 1750 by 25 using
an alternative approach or proceeded to process figures with little reason. Only a minority of
candidates obtained full marks.

Paper 5526
This was a more unusual question which aimed to test candidates understanding of the
relationship between a sample proportion and a population proportion. Some candidates did not
recognise it as such and so tried, for example, to calculate the mean. Other candidates clearly
did not understand the meaning of the table, itself and used the number of nails in the box (16)
as a way of answering the question.

15. Higher Tier

The virtually all of the candidates found part (a) a very straightforward introduction to the
paper. Most knew what was required and very few errors came from arithmetical slips.
In part (b), the majority of candidates used the expected method 0.2 × 200 or its equivalent, but
200/5, 200 × 1/5, 200 × 2/10 and 20% of 200 were also seen. A few candidates worked out how
many there were for each of the other colours and then subtracted from 200.
The most common errors here were to use the answer 0.4 from part (a); to divide 200 by 0.2; or
to give the probability that the counter will be red (20%).
Intermediate Tier
Part (a) was answered very well. Errors sometimes resulted from incorrect addition or incorrect
subtraction from 1. Some candidates made a mistake when attempting to write 0.4 as a fraction
and some wrote the correct probability in the table but then gave a different one on the answer
line. Part (b) was also answered well. Some of the candidates who knew that they needed to
multiply 200 by 0.2 were unable to perform the calculation correctly.

16. Foundation Tier

This question was well understood and candidates were usually able to score some marks on
this question, although the inability in some cases to fill in any of the numbers correctly in the
two-way table was surprising. Incorrect notation for probability such as 16 out of 40 and 16:40
were often seen. Other errors on this part of the question were words such as likely or unlikely.
Intermediate Tier
Part (a) was answered extremely well. Some candidates gave the number of white Toyota cars
rather than the total number of white cars. Only a handful of candidates failed to score any
marks in part (b) with most completing the two-way table correctly. More than 80% of
candidates gave the correct probability in part (c). Very few wrote a probability using incorrect
notation.
Edexcel GCSE Maths - Probability of Events (FH)

17. Foundation Tier

This question was well understood and candidates usually obtained full marks in part (a) though
in parts (b) and (c) candidates usually only wrote down partial solutions.
Intermediate Tier
Part (a) was answered very well indeed. Almost three quarters of the candidates were successful
in part (b). Some candidates only gave either (2, 3) or (3, 2) for the answer, not appreciating that
(dice 2, spinner 3) is different from (dice 3, spinner 2). Almost all candidates were able to list at
least three correct pairs in part (c). Some repeated pairs in reverse order, e.g. (2, 6) and (6, 2),
despite 4 being the highest number on the spinner, and some failed to list all the pairs. Some
candidates ignored “or more” and only listed the three pairs that give a score of 8. It was
common to see pairs such as (1, 7) that included impossible values.

18. Those candidates who were familiar with stem and leaf diagrams usually answered part (a) quite
well although many did not understand how to complete the key. Some candidates made no
attempt to order the leaves but many who did were careless and made one error in the ordering
or omitted one or two leaves. A significant number of candidates did not know what was meant
by a stem and leaf diagram and many tally charts and pictograms were seen. The probability in
part (b) was often correct even when the diagram in part (a) was incorrect or not attempted and
it was pleasing that most candidates expressed the probability in a correct form. Many
candidates did not understand that to find the number of teachers over 40 years old they must
5 5
include those over 50 as well so was a common incorrect answer. Some showed in their
15 15
1 1
working, gaining one mark, and then simplified it to but those who gave an answer of
3 3
with no working got no mark.

19. This was a well answered question with most candidates gaining full marks. A significant
minority gained only 1 mark since they gave their answer using incorrect probability notation,
for example giving their answer as a ratio, or using words “5 out of 12”. Centres are reminded
that probability can only be accepted when written as a fraction, a decimal or a percentage.
Some weaker candidates incorrectly added the 3, 4 and 5. The most common incorrect answer
5
was .
7

20. This question was done well by the vast majority of the candidates. Most knew that the sum of
the probabilities in the table should equal 1 and were able to work out the missing value 0.4.
Answers of 4/10 or 2/5 were not uncommon.
Edexcel GCSE Maths - Probability of Events (FH)

21. Overwhelmingly correct although there were some careless answers involving 3 + 4 + 5 = 11 or
13. A few candidates gave answers as ratios so could not score full marks and a few lost marks
in premature approximation when they converted their fraction to a decimal or to a percentage.

22. Foundation
Just over half the candidates gave correct answers, often given without any evidence of method.
The most common error was to use 0.02 instead of 0.2. Unfortunately many of these candidates
did not show their working and so scored no marks. A few worked in percentages but gave an
answer of 35 instead of 35%. Several simply divided 1 by 5 to give an answer of 0.2 and a few
seemed to treat the probabilities as a number sequence giving an answer of 0.3 from 0.2, 0.25
…….

Higher
Disappointingly, just over 14% of candidates were unable to gain any marks in this
straightforward question. Over 82% of candidates gained full marks. The most common error
was to make a mistake in the addition of the given probabilities.

23. Foundation
The two-way table in part (a) was usually completed accurately, although a number of
arithmetic errors were in evidence. In the table, the car column caused the most problems for
candidates.
37
In part (b), the correct answer of (or 0.37 or 37%) was the most common response.
100
Answers of 37 and 1/37 were also seen. There were also several who did not realise a numerical
answer was required, responding with “unlikely”
In part (c), most candidates scored at least one mark for using either 46 or 24 in their working.
Many failed to score full marks with answers of 1/46 and 24/100 being common errors. Some
failed to see “not”, giving an answer of 22/46. Following the correct answer in (b), many
63
candidates gave as their answer in (c), having not fully read the question correctly.
100
There were less candidates giving unacceptable notation but ratio and ‘out of’ were still seen on
several occasions.
Edexcel GCSE Maths - Probability of Events (FH)

Higher
Points were usually plotted correctly although a few candidates clearly missed this part of the
question. A number initially misread the table horizontally and so plotted (65, 80) but then
realised and rectified their mistake when unable to plot (100, 110) on the axes provided. In part
(b) the majority of candidates chose to describe a dynamic relationship along the lines of “the
taller the sheep, the longer it is” rather than just stating positive correlation. Incorrect answers
most commonly seen involved “direct proportion” or an expression of the difference between
the variables. A number referred to weight of sheep rather than height. In part (c) neither a line
of best fit nor vertical line at 76cm was usually seen. Instead candidates judged the value by eye
and in most cases gained full marks by being within the acceptable range of answers. Errors that
did occur were due to the 2 axes being confused or misreading of the vertical scale.

24. This question was answered well by the vast majority of candidates.
The most common errors in part (a) were due to the failure to carry out simple additions and
subtractions accurately with incorrect entries seen most often in the ‘Car’ column. Some
candidates failed to notice the empty space in the ‘Total’ column and left this blank. In these
cases it was apparent that candidates had not carried out a horizontal check as well as a vertical
one. The probability in part (b) was usually correct.

25. This question was very well done and a correct answer of 0.22 was seen with or without
working. However a significant number of candidates, making slight arithmetic errors, failed to
score at all because of the absence of a clear method.
Candidates electing to use percentages often lost a mark by failing to write the % sign.

26. Generally well answered although some candidates were confused by the (correct) use of the
word ‘estimate’ and worked out 400 × 0.5. Some candidates thought that they had to give the
160
answer in the form this does not make sense when read with the demand of the question. A
400
2
number of candidates then went further and simplified their expression to .
5

27. Part (a) of this question was very centre dependant, many centres showing evidence of not
having taught this topic at all. Those candidates who understood stem and leaf diagrams usually
gained 2 marks only, failing to give a key to their diagrams or leaving the leaves unordered.
Very many candidates were successful in part (b) although a significant number worked out
100 – 0.05 or 10 – 0.05. A few candidates read 0.05 as a half and offered the same as their
answer.
Edexcel GCSE Maths - Probability of Events (FH)

28. Very well done with few errors; most candidates gaining full marks. Only a small minority
failed to subtract “0.76” from 1.

29. Some candidates still continue to fail to write probability in a mathematical form opting instead
for a description, which usually incorporates various degrees of ‘likely’. Answers of ‘4 in 9’ or
‘4 out of 9’ gained only one mark. Writing probability as the ratio 4 : 9 scored no marks. The
4
most common incorrect answer was .
5

30. Candidates should be made aware that, in the context of probability, ‘estimate’ does not mean
‘approximate’. A very common error was to use 0.25 or 0.2 instead of 0.24 sometimes without
any earlier reference to 0.24. It was disappointing to see answers greater than 300.

31. Another successfully answered question with only a quarter failing to score. The most common
error was to give 0.29 as the sum of the probabilities, followed by an answer of 0.71. This
gained one mark provided that the full working was shown. A few wrote 0.45 as the difference
between 1 and 0.65. 0.3 + 0.1 + 0.25 = 0.425 was often seen.

32. The majority of candidates (71%) gained full marks here and a further 13% gained one mark
usually for an answer of 0.56 (1 – 0.03 – 0.17 – 0.24) found without the use of a calculator.
Failure to score any marks was either through a lack of understanding or going no further than
to add the probabilities giving an answer of 0.71 or 0.44

33. Many candidates realised they had to subtract the given numbers from 1 but as they did not
show their working or because they did not use a calculator, only a quarter of the candidates
scored both marks. 20% of the candidates scored one mark, mostly by writing 0.49 (a special
case mark for those candidates who added the 0.2 as 0.02) or writing the digits 31.

34. Part (a) was generally well done, however 0.8 (using 5. 0 + 15. 0 = 2.0 ) was the
most common error.
Many candidates scored full marks in part (b) but misunderstanding often led to an answer of
23 8 31
“ or ” appearing on the answer line. 31, 31% and were common incorrect answers.
50 50 100
Edexcel GCSE Maths - Probability of Events (FH)

35. No report available.

36. This question was answered correctly by the vast majority of candidates. A very small minority
of candidates misread the question and gave an estimate for the number of adults who did not
vote in an election. Some candidates misinterpreted the word ‘estimate’ to mean that they had
calculate an estimate to 0.7 × 20000 and so evaluated with 0.5 × 20000 or 0.75 × 20000 such an
approach did not gain any credit. The other common error was to attempt to evaluate 20000 ÷
0.7.

37. The probability appeared written as a fraction in a large proportion of the working seen but there
were still expressions such as ‘likely’ scoring no marks where this was given alone. Some gave
the probability of obtaining a ‘2’ as ‘2/6’ and ‘3’ as ‘3/6’ and combined them together to
produce variations of ‘2/6,3/6’ or ‘5/6’ as the final answer. Those who perhaps gave more
thought to each outcome came up with ‘1/6’ as the required individual probability and scored
1mark for showing this fraction. Combining together the two ‘1/6’ values proved to be
troublesome. A more logical approach might have been to consider taking the two events out of
a total of six and writing the fraction as ‘2/6’ directly. Giving the final answer in the form ‘2 out
of 6’, or similar, received only a method mark for identifying the ‘2’ and the ‘6’. Some
statements were seen which tried to resolve the issue with ‘it might but it might not’ offering a
flavour of the more bizarre. Around 56% of the candidates scored both available marks.

38. This question was well understood with 97% of candidates correctly answering the question. A
very small minority forgot to take the total probability away from 1 and an even smaller
minority forgot to write their working.

39. Just under 60 % of the candidates scored full marks in this question.
However, “0.35” was often seen, apparently derived by candidates using a number sequence
approach or one based on symmetry. A significant minority of candidates, who did not have
access to a calculator or preferred not to use one, and who recorded a fully correct method, were
able to gain 1 mark. These candidates were often unable to add the three given probabilities or
subtract their total from 1 with accuracy.

40. This question was well answered with 70% of candidates scoring 2 marks. A small minority of
candidates described the likelihood of taking a black pencil, or gave a word or phrase instead of
the answer (⅜ or equivalent) required. It is good to report that few candidates gave the
probability in an unacceptable form or as a whole number.
Edexcel GCSE Maths - Probability of Events (FH)

41. Part (a) was answered well by the vast majority of the candidates.
Part (b) was answered well by most candidates. A common error here was to write the final
answer as 10/50 (typically) or 10/100 (rarely).

42. Calculating the missing probability in the opening question did not pose too much of a problem
with many correct answers seen. For those who did make a mistake the addition 0.5 + 0.3
leading to 0.9, 0.08, or similar was still rewarded as long as the subtraction 1 – (0.5 + 0.3) was
shown in the working thus gaining the method mark.
In part (b) calculating how many green counters were in the bag needed an appreciation that the
product 50 × 0.3 would yield the correct result. The more successful ones were able to indicate
this product correctly but a few found difficulties in evaluating the result. It gave rise to answers
involving the digits 1 and 5 with 0.15 and 150 being the most common. The most common other
errors, however, occurred in using the probability from part (a) as answers were given for the
blue counter rather than the green one as had been asked in the question. Also, some candidates
spent needless time calculating the amount for each colour, and then often failed to identify the
one required in the question. Nearly 70% of the candidates scored all 4 marks with around 25%
scoring 2 marks.

43. On this paper we did not test the drawing of a pie chart, instead we gave candidates a pie chart
and asked them to interpret it.
Parts (a)(i) and (ii) were both correct in 35% of cases. The mark-scheme was set up to accept
answers written as fractions, decimals and percentages but 1 mark compensation was given for
those candidates that wrote both answers as 1 out of 4 and 3 out of 4. We also allowed one mark
in part (a)(ii) for those candidates that wrote an answer that was 1 – their answer to a(i). No
marks at all were awarded for those candidates that wrote any of their probabilities as ratios as a
ratio of 1:4 or 3:4 are probabilities out of 5 and 7 respectively.
In part (b), only 30% of candidates scored full marks for an answer of 72. One mark was
awarded for a method that realised that 30º was a twelfth of 360º or one person was represented
by 5º or for a partial method to add at least 3 correct frequencies out of the five; 8% gained this
method mark which more candidates could have gained this method mark if they had shown
their attempt to add.

44. This question proved to be very successful with 55% of candidates being able to write out the
missing 17 combinations successfully. One mark was obtained by 25% of candidates that could
give an additional 6 outcomes but 20% scored no marks. Interestingly a significant number of
candidates thought there were only 3 numbers on the dice since only 1, 2 and 3 were shown in
the diagram. The most successful candidates gave their combinations in an ordered fashion,
either by all the greens followed by all the blues followed by all the reds or by all the ones, all
the twos etc.
Edexcel GCSE Maths - Probability of Events (FH)

45. This question was very well understood with 76% gaining all four marks in part (a) and (b).
Partial credit was given for those who wrote their probabilities incorrectly and for those who
thought that 1 – (0.35 + 0.1 + 0.3) was 1 – 0.39 and wrote 0.61 as their answer for part (a) and
that 0.35 + 0.1 was equal to 0.36 in part (b). However, a number of candidates showed no
working, and so a wrong answer of 0.61 in part (a) scored no marks. In part (b) the most
common error was to multiply 0.1 and 0.35 together instead of adding. There were also a
significant number of candidates who hadn’t read the question carefully enough, and added the
probabilities for green and red, rather than yellow and red. In part (c) the question was well
answered by most candidates with 78% scoring both marks whilst those that wrote 0.3 × 200
scored 1 mark as did those who wrote the answer as 60/200. The vast majority of those who
scored no marks did so because they divided 200 by 0.3, instead of multiplying.
Edexcel GCSE Maths - Probability of Events (H)

1. Julie does a statistical experiment. She throws a dice 600 times.

She scores six 200 times.

(a) Is the dice fair? Explain your answer.

.............................................................................................................................

..............................................................................................................................
(1)

Julie then throws a fair red dice once and a fair blue dice once.

(b) Complete the probability tree diagram to show the outcomes.

Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.

Red Blue
Dice Dice

1
Six
6

Not
Six
(3)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

2. A bag contains 3 black beads, 5 red beads and 2 green beads.

Gianna takes a bead at random from the bag, records its colour and replaces it.
She does this two more times.

Work out the probability that, of the three beads Gianna takes, exactly two are
the same colour.

.................................
(Total 5 marks)

3. Julie does a statistical experiment. She throws a dice 600 times.

She scores six 200 times.

(a) Is the dice fair? Explain your answer.

.....................................................................................................................................

.....................................................................................................................................
(1)
Edexcel GCSE Maths - Probability of Events (H)

Julie then throws a fair red dice once and a fair blue dice once.

(b) Complete the probability tree diagram to show the outcomes.

Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.

Red Blue
Dice Dice

1
Six
6

Not
Six
(3)

(c) (i) Julie throws a fair red dice once and a fair blue dice once. Calculate the probability
that Julie gets a six on both the red dice and the blue dice.

....................................

(ii) Calculate the probability that Julie gets at least one six.

.....................................
(5)
(Total 9 marks)
Edexcel GCSE Maths - Probability of Events (H)

4. The probability that Betty will be late for school tomorrow is 0.05
The probability that Colin will be late for school tomorrow is 0.06

The probability that both Betty and Colin will be late for school tomorrow is 0.011

Fred says that the events ‘Betty will be late tomorrow’ and ‘Colin will be late tomorrow’ are
independent.

Justify whether Fred is correct or not.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................
(Total 2 marks)

5. Mathstown College has 500 students, all of them in the age range 16 to 19.
The incomplete table shows information about the students.

Number of Number of
Age (years) male students female students
16 50 30
17 60 40
18 76 54
19

A newspaper reporter is carrying out a survey into students’ part-time jobs.

She takes a sample, stratified both by age and by gender, of 50 of the 500 students.

(a) Calculate the number of 18 year old male students to be sampled.

…………………………
(3)
Edexcel GCSE Maths - Probability of Events (H)

In the sample, there are 9 female students whose age is 19 years.

(b) Work out the least number of 19 year old female students in the college.

…………………………
(2)

A newspaper photographer is going to take photographs of two students from Mathstown

College.

He chooses
one student at random from all of the 16 year old students and
one student at random from all of the 17 year old students.

(c) Calculate the probability that he will choose two female students.

…………………………
(3)
(Total 8 marks)
Edexcel GCSE Maths - Probability of Events (H)

6. Joan has two boxes of chocolates.

The boxes are labelled A and B.

Box A contains 15 chocolates. There are 6 plain, 4 milk and 5 white chocolates.
Box B contains 12 chocolates. There are 4 plain, 3 milk and 5 white chocolates.

Joan takes one chocolate at random from each box.

Work out the probability that the two chocolates Joan takes are not of the same type.

………………………………
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

7. Amy has 10 CDs in a CD holder.

Amy’s favourite group is Edex.
She has 6 Edex CDs in the CD holder.

Amy takes one of these CDs at random.

She writes down whether or not it is an Edex CD.
She puts the CD back in the holder.
Amy again takes one of these CDs at random.

(a) Complete the probability tree diagram.

First choice Second choice EDEX

CD
..........

EDEX
CD NOT-EDEX
0.6 ..........
CD
EDEX
CD
..........
.......... NOT-EDEX
CD

.......... NOT-EDEX
CD
(2)

Amy had 30 CDs.

The mean playing time of these 30 CDs was 42 minutes.

Amy sold 5 of her CDs.

The mean playing time of the 25 CDs left was 42.8 minutes.

(b) Calculate the mean playing time of the 5 CDs that Amy sold.

......................... minutes
(3)
(Total 5 marks)
Edexcel GCSE Maths - Probability of Events (H)

8. The probability that a biased dice will land on a four is 0.2

Pam is going to roll the dice 200 times.

The probability that a biased dice will land on a six is 0.4

Ted rolls the biased dice once.

Work out the probability that the dice will land on either a four or a six.

.........................
(Total 2 marks)

9. (a) (ii) Factorise 2x2 – 35x + 98

...................................

(ii) Solve the equation 2x2 – 35x + 98 = 0

....................................
(3)
Edexcel GCSE Maths - Probability of Events (H)

A bag contains (n + 7) tennis balls.

n of the balls are yellow.
The other 7 balls are white.

John will take at random a ball from the bag.

He will look at its colour and then put it back in the bag.

(b) (i) Write down an expression, in terms of n, for the probability that John will take a
white ball.

....................................

2
Bill states that the probability that John will take a white ball is
5

(ii) Prove that Bill’s statement cannot be correct.

(3)
Edexcel GCSE Maths - Probability of Events (H)

After John has put the ball back into the bag, Mary will then take at random a ball from the bag.
She will note its colour.

4
(c) Given that the probability that John and Mary will take balls with different colours is ,
9
prove that 2n2 – 35n + 98 = 0

(5)
Edexcel GCSE Maths - Probability of Events (H)

(d) Using your answer to part (a) (ii) or otherwise, calculate the probability that John and
Mary will both take white balls.

....................................
(2)
(Total 13 marks)

10. Amy has 10 CDs in a CD holder.

Amy’s favourite group is Edex.
She has 6 Edex CDs in the CD holder.

Amy takes one of these CDs at random.

She writes down whether or not it is an Edex CD.
She puts the CD back in the holder.
Amy again takes one of these CDs at random.

(a) Complete the probability tree diagram.

First choice Second choice EDEX

CD
..........

EDEX
CD NOT-EDEX
0.6 ..........
CD
EDEX
CD
..........
.......... NOT-EDEX
CD

.......... NOT-EDEX
CD
(2)
Edexcel GCSE Maths - Probability of Events (H)

(b) Find the probability that Amy will pick two Edex CDs.

.....................
(2)

Amy had 30 CDs.

The mean playing time of these 30 CDs was 42 minutes.

Amy sold 5 of her CDs.

The mean playing time of the 25 CDs left was 42.8 minutes.

(c) Calculate the mean playing time of the 5 CDs that Amy sold.

......................... minutes
(3)
(Total 7 marks)
Edexcel GCSE Maths - Probability of Events (H)

11. Tony throws a biased dice 100 times.

The table shows his results.

Score Frequency
1 12
2 13
3 17
4 10
5 18
6 30

He throws the dice once more.

(a) Find an estimate for the probability that he will get a 6.

.....................................
(1)

Emma has a biased coin.

The probability that the biased coin will land on a head is 0.7
Emma is going to throw the coin 250 times.

(b) Work out an estimate for the number of times the coin will land on a head.

.....................................
(2)
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (H)

12. In a game of chess, you can win, draw or lose.

Gary plays two games of chess against Mijan.

The probability that Gary will win any game against Mijan is 0.55
The probability that Gary will win draw game against Mijan is 0.3

(a) Work out the probability that Gary will win exactly one of the two games against Mijan.

..................................
(3)
Edexcel GCSE Maths - Probability of Events (H)

In a game of chess, you score

1 point for a win

1
point for a draw,
2
0 points for a loss.

(b) Work out the probability that after two games, Gary’s total score will be the same as
Mijan’s total score.

..................................
(3)
(Total 6 marks)
Edexcel GCSE Maths - Probability of Events (H)

13. Amy is going to play one game of snooker and one game of billiards.

3
The probability that she will win the game of snooker is
4

1
The probability that she will win the game of billiards is
3

Complete the probability tree diagram.

(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (H)

14. Amy is going to play one game of snooker and one game of billiards.

3
The probability that she will win the game of snooker is
4

1
The probability that she will win the game of billiards is
3

(a) Complete the probability tree diagram.

(2)
Edexcel GCSE Maths - Probability of Events (H)

(b) Work out the probability that Amy will win exactly one game.

…………………….
(3)

Amy played one game of snooker and one game of billiards on a number of Fridays.
She won at both snooker and billiards on 21 Fridays.

(c) Work out an estimate for the number of Fridays on which Amy did not win either game.

…………………….
(3)
(Total 8 marks)
Edexcel GCSE Maths - Probability of Events (H)

15. Jeremy designs a game for a school fair.

He has two 5-sided spinners.

The spinners are equally likely to land on each of their sides.

One spinner has 2 red sides, 1 green side and 2 blue sides.

The other spinner has 3 red sides, 1 yellow side and 1 blue side.

(a) Calculate the probability that the two spinners will land on the same colour.

………………….
(3)

The game consists of spinning each spinner once.

It costs 20p to play the game.

To win a prize both spinners must land on the same colour.

The prize for a win is 50p.

100 people play the game.

Edexcel GCSE Maths - Probability of Events (H)

(b) Work out an estimate of the profit that Jeremy should expect to make.

£…………………
(2)
(Total 5 marks)
Edexcel GCSE Maths - Probability of Events (H)

16. Loren has two bags.

The first bag contains 3 red counters and 2 blue counters.
The second bag contains 2 red counters and 5 blue counters.

Loren takes one counter at random from each bag.

Complete the probability tree diagram.

Counter from Counter from

first bag second bag

Red
2
7

Red
3
5
......
Blue

Red
......
......
Blue

......
Blue

(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (H)

17. Loren has two bags.

The first bag contains 3 red counters and 2 blue counters.
The second bag contains 2 red counters and 5 blue counters.

Loren takes one counter at random from each bag.

(a) Complete the probability tree diagram.

Counter from Counter from

first bag second bag

Red
2
7

Red
3
5
......
Blue

Red
......
......
Blue

......
Blue
(2)
Edexcel GCSE Maths - Probability of Events (H)

(b) Work out the probability that Loren takes one counter of each colour.

...............................................
(3)
(Total 5 marks)

18. (a) Solve the equation 19x2 – 124x – 224 = 0

x = .......................... , x = ..........................
(3)

A bag contains red counters and blue counters and white counters.

There are n red counters.

There are 2 more blue counters than, red counters.
The number of white counters is equal to the total number of red counters and blue counters.

(b) Show that the number of counters in the bag is 4(n + 1)

(1)
Edexcel GCSE Maths - Probability of Events (H)

Bob and Ann play a game.

Bob will take a counter at random from the bag.

He will record the colour and put the counter back in the bag.
Ann will then take a counter at random from the bag.
She will record its colour.
14
The probability that Bob’s counter is red and Ann’s counter is not red is
81

(c) Prove that 19n2 – 124n – 224 = 0

(5)

(d) Using your answer to part (a), or otherwise, show that the number of counters in the bag
is 36

(1)
Edexcel GCSE Maths - Probability of Events (H)

Bob and Ann play the game with all 36 counters in the bag.

(e) Calculate the probability that Bob and Ann will take counters with different colours.

.....................................
(3)
(Total 13 marks)

19. Simon plays one game of tennis and one game of snooker.

3
The probability that Simon will win at tennis is
4

1
The probability that Simon will win at snooker is
3
Edexcel GCSE Maths - Probability of Events (H)

Complete the probability tree diagram.

tennis snooker

1 Simon
3 wins

Simon
wins
3
4 Simon
.......... does not
win

Simon
.......... wins
Simon
.......... does not
win
Simon
.......... does not
win
(Total 2 marks)

20. Simon plays one game of tennis and one game of snooker.

3
The probability that Simon will win at tennis is
4

1
The probability that Simon will win at snooker is
3
Edexcel GCSE Maths - Probability of Events (H)

(a) Complete the probability tree diagram below.

tennis snooker

1 Simon
3 wins

Simon
wins
3
4 Simon
.......... does not
win

Simon
.......... wins
Simon
.......... does not
win
Simon
.......... does not
win

(2)

(b) Work out the probability that Simon wins both games.

.....................................
(2)

(c) Work out the probability that Simon will win only one game.

.....................................
(3)
(Total 7 marks)
Edexcel GCSE Maths - Probability of Events (H)

21. Mary has a drawing pin.

When the drawing pin is dropped it can land either ‘point up’ or ‘point down’.
The probability of it landing ‘point up’ is 0.4

Mary drops the drawing pin twice.

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that the drawing pin will land ‘point up’ both times.

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

22. The probability that any piece of buttered toast will land buttered side down when it is dropped
is 0.62
Two pieces of buttered toast are to be dropped, one after the other.

Calculate the probability that exactly one piece of buttered toast will land buttered side down.

......................................
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

23. There are two sets of traffic lights on Georgina’s route to school.
The probability that the first set of traffic lights will be red is 0.4
The probability that the second set of traffic lights will be red is 0.3

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that both sets of traffic lights will be red.

.....................................
(2)
Edexcel GCSE Maths - Probability of Events (H)

(c) Work out the probability that exactly one set of traffic lights will be red.

.....................................
(3)
(Total 7 marks)

24. Martin has a pencil case which contains 4 blue pens and 3 green pens.

Martin picks a pen at random from the pencil case. He notes its colour, and then replaces it.
He does this two more times.

Work out the probability that when Martin takes three pens, exactly two are the same colour.

.................................
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (H)

25. Julie has 100 music CDs.

58 of the CDs are classical.
22 of the CDs are folk.
The rest of the CDs are jazz.

On Saturday, Julie chooses one CD at random from the 100 CDs.

On Sunday, Julie chooses one CD at random from the 100 CDs.

(a) Complete the probability tree diagram.

(2)

Saturday Sunday
Classical
...........

........... Folk
Classical

........... Jazz
0.58
Classical
...........
0.22 ...........
Folk Folk

........... Jazz
Classical
........... ...........
Jazz ........... Folk

...........
Jazz

(b) Calculate the probability that Julie will choose a jazz CD on both Saturday and
Sunday.

...................................
(2)
Edexcel GCSE Maths - Probability of Events (H)

(c) Calculate the probability that Julie will choose at least one jazz CD on Saturday and
Sunday.

...................................
(3)
(Total 7 marks)

26. Tom and Sam each take a driving test.

The probability that Tom will pass the driving test is 0.8

The probability that Sam will pass the driving test is 0.6

(a) Complete the probability tree diagram.

Tom Sam

0.6 Pass

Pass
0.8
............... Fail

0.6 Pass
...............
Fail

............... Fail
(2)

(b) Work out the probability that both Tom and Sam will pass the driving test.

.......................................................
(2)
Edexcel GCSE Maths - Probability of Events (H)

(c) Work out the probability that only one of them will pass the driving test.

.......................................................
(3)
(Total 7 marks)

27. Matthew puts 3 red counters and 5 blue counters in a bag.

He takes at random a counter from the bag.
He writes down the colour of the counter.
He puts the counter in the bag again.
He then takes at random a second counter from the bag.

(a) Complete the probability tree diagram.

1st counter 2nd counter

3
8 Red

3 Red
8
........ Blue

........ Red

........
Blue

........ Blue
(2)
Edexcel GCSE Maths - Probability of Events (H)

(b) Work out the probability that Matthew takes two red counters.

..........................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

28. In a game of chess, a player can either win, draw or lose.

The probability that Vishi wins any game of chess is 0.5

The probability that Vishi draws any game of chess is 0.3

Vishi plays 2 games of chess.

(a) Complete the probability tree diagram.

1st game 2nd game

............... Win

...............
Win Draw

Lose
0.5 ...............

............... Win

0.3 ...............
Draw Draw

Lose
...............

............... ............... Win

...............
Lose Draw

Lose
...............
(2)
Edexcel GCSE Maths - Probability of Events (H)

(b) Work out the probability that Vishi will win both games.

.....................................
(2)
(Total 4 marks)

29. Phil has 20 sweets in a bag.

5 of the sweets are orange.

7 of the sweets are red.
8 of the sweets are yellow.

Phil takes at random two sweets from the bag.

Work out the probability that the sweets will not be the same colour.

................................................
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

30. Julie and Pat are going to the cinema.

The probability that Julie will arrive late is 0.2

The probability that Pat will arrive late is 0.6
The two events are independent.

(a) Complete the diagram.

Pat

late
0.6
Julie

late
0.2
not
late

late

not
late

not
late
(2)

(b) Work out the probability that Julie and Pat will both arrive late.

……………………………
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

31. Salika travels to school by train every day.

The probability that her train will be late on any day is 0.3

(a) Complete the probability tree diagram for Monday and Tuesday.

Monday Tuesday
0.3 late

late
0.3
not
late

late

not
late
not
late
(2)

(b) Work out the probability that her train will be late on at least one of these two days.

……………………………
(3)
(Total 5 marks)
Edexcel GCSE Maths - Probability of Events (H)

32. A bag contains 3 black beads, 5 red beads and 2 green beads.
Gianna takes a bead at random from the bag, records its colour and replaces it.
She does this two more times.

Work out the probability that, of the three beads Gianna takes, exactly two are the same
colour.

...............................
(Total 5 marks)

33. Daniel took a sample of 100 pebbles from Tawny Beach.

He weighed each pebble and recorded its weight.
He used the information to draw the cumulative frequency graph shown on the grid.

(a) Use the cumulative frequency graph to find an estimate for

(i) the median weight of these pebbles,

.............................. grams

(ii) the number of pebbles with a weight more than 60 grams.

.........................................
(3)
Edexcel GCSE Maths - Probability of Events (H)

Cumulative
Frequency

120

100

80

60

40

20

O
10 20 30 40 50 60 70 80
Weight (grams)

Daniel also took a sample of 100 pebbles from Golden Beach.

The table shows the distribution of the weights of the pebbles in the sample from Golden Beach.

Weight (w grams) Cumulative frequency

0 < w ≤ 20 1
0 < w ≤ 30 15
0 < w ≤ 40 36
0 < w ≤ 50 65
0 < w ≤ 60 84
0 < w ≤ 70 94
0 < w ≤ 80 100

(b) On the same grid, draw the cumulative frequency graph for the information shown in the
table.
(2)
Edexcel GCSE Maths - Probability of Events (H)

Daniel takes one pebble, at random, from his sample from Tawny Beach and one pebble, at
random, from his sample from Golden Beach.

(c) Work out the probability that the weight of the pebble from Tawny Beach is more than
60 grams and the weight of the pebble from Golden Beach is more than 60 grams.

.....................................
(4)
(Total 9 marks)
Edexcel GCSE Maths - Probability of Events (H)

34. Jim spins a biased coin.

The probability that it will land on heads is twice the probability that it will land on tails.

Jim spins the coin twice.

Find the probability that it will land once on heads and once on tails.

……………………
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

35. Jacob has 2 bags of sweets.

Bag P Bag Q

Bag P contains 3 green sweets and 4 red sweets.

Bag Q contains 1 green sweet and 3 yellow sweets.

Jacob takes one sweet at random from each bag.

(a) Complete the tree diagram.

Bag P Bag Q

green

3 green
7
yellow

green

red

yellow
(2)
Edexcel GCSE Maths - Probability of Events (H)

(b) Calculate the probability that Jacob will take 2 green sweets.

………………….
(2)
(Total 4 marks)

36. Tony designs a game.

It costs £1.20 to play the game.

3
The probability of winning the game is
10

The prize for each win is £2.50

150 people play the game.

Work out an estimate of the profit that Tony should expect to make.

£ ..............................
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

37. Amy is going to play one game of snooker and one game of billiards.
1
The probability that she will win the game of snooker is
3
3
The probability that she will win the game of billiards is
4
The probability tree diagram shows this information.

Amy played one game of snooker and one game of billiards on a number of Fridays.
She won at both snooker and billiards on 21 Fridays.

Work out an estimate for the number of Fridays on which Amy did not win either game.

…………
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (H)

38. Lucy and Jessica take a test.

The probability that Lucy will pass the test is 0.7

The probability that Jessica will pass the test is 0.4

(a) Complete the probability tree diagram.

Lucy Jessica
pass
0.4

pass
0.7
fail
pass

fail

fail
(2)

(b) Work out the probability that only one of the 2 girls will pass the test.

..............................
(3)
(Total 5 marks)
Edexcel GCSE Maths - Probability of Events (H)

39. Stuart is taking a French exam and an art exam.

The probability that Stuart will pass the French exam is 0.7
The probability that Stuart will pass the art exam is 0.8

Work out the probability that Stuart will pass exactly one of these exams.

.....................................
(Total 3 marks)

40. A spinner can land on Red or White or Blue.

The table shows the probability that the spinner will land on Red or on White.

Colour Red White Blue

Probability 0.3 0.25

(a) Work out the probability that the spinner will land on Blue.

.....................................
(2)

Sam is going to spin the spinner 200 times.

(b) Work out an estimate for the number of times the spinner will land on Red.

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

41. There are 9 stones in a bag.

4 stones are blue.
5 stones are green.

Lisa takes a stone at random from the bag.

She does not replace it.
She then takes at random a second stone from the bag.

Work out the probability that at least one of these two stones is blue.

.....................................
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (H)

42. Sunita plays a game of chess.

She can win or draw or lose the game.

The table shows each of the probabilities that she will win or draw the game.

Result Win Draw Lose

Probability 0.6 0.3

Work out the probability that she will lose the game.

.....................................
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (H)

43. There are 3 boys and 7 girls at a playgroup.

Mrs Gold selects two children at random.

(a) Complete the probability tree diagram below.

1st child 2nd child

boy
............

3 boy
10 ............ girl

boy
............
............ girl

girl
............
(2)

(b) Work out the probability that Mrs Gold selects two girls.

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

44. Caroline cycles to school.

She passes through two sets of traffic lights.

2
The probability that she has to stop at the first set of traffic lights is
5

If she has to stop at the first set of traffic lights, the probability that she has to stop

5
at the second set is
6

If she does not have to stop at the first set of traffic lights, the probability that she has to

1
stop at the second set is
2

Caroline cycles to school on the last day of term.

Work out the probability that she has to stop at only one set of traffic lights.

.....................................
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

45. Ivan plays a game of darts and a game of snooker.

3
The probability that he will win at darts is
7

6
The probability that he will win at snooker is
11

Complete the probability tree diagram.

Darts Snooker

6
11 Win

3
7 Win

.............. Not Win

.............. Win

Not Win

..............

Not Win
..............
(Total 2 marks)
Edexcel GCSE Maths - Probability of Events (H)

46. There are 3 strawberry yoghurts, 2 peach yoghurts and 4 cherry yoghurts in a fridge.

Kate takes a yoghurt at random from the fridge.

She eats the yoghurt.
She then takes a second yoghurt at random from the fridge.

Work out the probability that both the yoghurts were the same flavour.

.....................................
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

47. Marco has a 4-sided spinner.

The sides of the spinner are numbered 1, 2, 3 and 4
The spinner is biased.

3
2

1
The table shows the probability that the spinner will land on each of the numbers 1, 2 and 3

Number 1 2 3 4

Probability 0.20 0.35 0.20

(a) Work out the probability that the spinner will land on the number 4

.....................................
(2)
Edexcel GCSE Maths - Probability of Events (H)

Marco spins the spinner 100 times.

(b) Work out an estimate for the number of times the spinner will land on the number 2

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

48. There are 8 pencils in a box.

5 pencils are blue.

3 pencils are red.

Simon takes a pencil at random from the box.

He does not replace the pencil.
Hazel then takes a pencil at random from the box.

Work out the probability that both Simon and Hazel take a red pencil.

.....................................
(Total 3 marks)
Edexcel GCSE Maths - Probability of Events (H)

49. Sue wants to find out if a 6-sided dice is biased.

She rolls the dice six times.

The table shows her results.

Score 1 2 3 4 5 6
Frequency 0 1 1 1 1 2

Sue says

“My experiment shows this dice is biased”.

Sue is wrong.
Explain why.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................
(Total 1 mark)

50. Nicola is going to travel from Swindon to London by train.

1
The probability that the train will be late leaving Swindon is
5

7
If the train is late leaving Swindon, the probability that it will arrive late in London is
10

1
If the train is not late leaving Swindon, the probability that it will arrive late in London is
10
Edexcel GCSE Maths - Probability of Events (H)

(a) Complete the probability tree diagram.

leaves Swindon arrives in London

late
............

1 late
5 ............ not late

late
............
............ not late

............ not late

(2)

(b) Work out the probability that Nicola will arrive late in London.

..........................
(3)
(Total 5 marks)
Edexcel GCSE Maths - Probability of Events (H)

51. William has two 10-sided spinners.

The spinners are equally likely to land on each of their sides.

BLUE RED BLUE RED

RED BLUE
GREEN BLUE
BLUE RED GREEN BLUE

RED BLUE
BLUE BLUE
GREEN RED BLUE RED

A B

Spinner A has 5 red sides, 3 blue sides and 2 green sides.

Spinner B has 2 red sides, 7 blue sides and 1 green side.

William spins spinner A once.

He then spins spinner B once.

Work out the probability that spinner A and spinner B do not land on the same colour.

..........................
(Total 4 marks)
Edexcel GCSE Maths - Probability of Events (H)

52. There are 4 bottles of orange juice,

3 bottles of apple juice,
2 bottles of tomato juice.

Viv takes a bottle at random and drinks the juice.

Then Caroline takes a bottle at random and drinks the juice.

Work out the probability that they both take a bottle of the same type of juice.

....................................
(Total 4 marks)

01. (a) No, as you would expect about 100.

Yes, as it is possible to get 200 sixes with a fair dice 1
B1 for a consistent answer

(b) 3
1 5
, + labels
6 6
5
B1 for on the red dice, not six branch
6
B1 for a fully complete tree diagram with all branches labelled
1 5
B1 for , on all remaining branches as appropriate
6 6
[4]
Edexcel GCSE Maths - Probability of Events (H)

660
02. oe 5
1000
Total = 3 + 5 + 2 (= 10)
3 3 5  45  3 3 2  18 
× × = , × × = 
10 10 10  1000  10 10 10  1000 
5 5 3  75  5 5 2  50 
× × = , × ×  = 
10 10 10  1000  10 10 10  1000 
2 2 3  12  2 2 5  20 
× × = , × ×  = 
10 10 10  1000  10 10 10  1000 
 "45" "18" "75" "50" "12" "20" 
3×  + + + + + 
 1000 1000 1000 1000 1000 1000 
660
1000
M3 for all six expressions seen OR their combined equivalents
(M2 for four expressions seen OR their combined equivalents)
(M1 for two expressions seen OR their combined equivalents)
M1 sum of 18 relevant products condone 1 slip
660
A1 for oe
1000
SC: without replacement maximum M4 A0
38 28
SC: Just 2 beads: Answer either oe OR oe B1
100 90
[5]

03. (a) No, as you would expect about 100.

Yes, as it is possible to get 200 sixes with a fair dice 1
B1 for a consistent answer
(b) 3
1 5
, + labels
6 6
5
B1 for on the red dice, not six branch
6
B1 for a fully complete tree diagram with all branches labelled
1 5
B1 for and on all remaining branches as appropriate
6 6
Edexcel GCSE Maths - Probability of Events (H)

1
(c) (i) 2
36
2
1
 
6
2
1 1 1
M1   or × only or 0.28
6  6 6
1
A1 or 0.03 or better
36

11
(ii) 3
36
2
5
1−  
6
OR
1 5 5 1 1 1
× + × + ×
6 6 6 6 6 6
2
5 5 5
M2 for 1 −   or 1 – ×
6  6 6
A1 cao
OR
1 5
M1 for × oe
6 6
1 5 5 1
M1 for 2 or 3 only of × , × , “a”
6 6 6 6
11
A1 for or 0.31 or better
36
[9]

04. No 2
0.06 × 0.05 = 0.003
M1 for 0.06 × 0.05
A1 correct conclusion based on 0.003 or 0.06 × 0.05
stated as ≠ 0.0011
OR M1 for statement that for the two events to be independent
P (BL and CL) = P(BL) × P(CL)
[2]
Edexcel GCSE Maths - Probability of Events (H)

05. (a) 8 3
50
× 76
500
50
M1 for × 76 oe
500
A2 cao
(A1 for 7.6)

(b) 86 2
9 × 10 or 90 or 8.5 × 10
M1 for 9 × 10 or 90 or 8.5 × 10 or 8.6 × 10 seen
A1 for either 86 or for 85

3
(c) 20 3

30 40
80 100
3 2
8×5
30 40
B1 for or oe seen
80 100
M1 for multiplying only two probabilities or full relevant
complete method
3
A1 oe
20
[8]
Edexcel GCSE Maths - Probability of Events (H)

119
06. 4
180

6 3 6 5 48
× + × =
15 12 15 12 180
4 4 4 5 36
× + × =
15 12 15 12 180
5 4 5 3 35
× + × =
15 12 15 12 180
Or
6 4 4 3 5 5
1−
15 × 12 + 15 × 12 + 15 × 12 
61
= 1−
180
M1 for sight of any 2 correct uses of the 6 cases
M1 for sight of remaining 4 correct uses of the 6 cases
M1 (dep on at least 3 correct terms) for adding 5 or 6 correct
terms
A1 cao
M1 for use of complimentary event
M1 for sight of any 2 correct terms
6 4 4 3 5 5
M1 for 1 −  × + × + × 
 15 12 15 12 15 12 
A1 cao
[4]

07. (a) 0.4, 0.6

0.4, 0.6,
0.4 2
B1 for LHS: (0.6), 0.4
B1 for RHS: 0.6, 0.4, 0.6, 0.4
(b) 38 3
(30 × 42) – (25 × 42.8) = 1260 – 1070 = 190
190 ÷ 5 =
M1 for (30 × 42) – (25 × 42.8) or 1260 – 1070 or 190 seen
M1 (dep) for “190” ÷ 5
A1 cao
[5]
Edexcel GCSE Maths - Probability of Events (H)

08. 0.6 2
0.2 + 0.4
M1 for 0.2 + 0.4
A1 for 0.6
[2]

09. (a) (i) (2x – 7)(x – 14) 3

M1 x2 term and constant term (± 98 obtained
or 2x(x – 14) – 7(x – 14) or x(2x – 7) – 14(2x – 7)
A1 for (2x – 7)(x – 14)

7
(ii) x= ; x = 14
2
B1ft ft (i) provided of form (2x ± a)(x ± b)

7
(b) (i) 3
n+7
7
B1 for oe
n+7
(ii) n=10.5 is not possible since n has to be an integer
7 2
= ⇒ 2(n + 7)= 5 × 7
n+7 5
2n = 21
M1 for 2(n + 7)= 5 × 7 or n+7=5 × 3.5 (can be implied) ft
(b)(i) fractional in terms of n and < 1
A1 ft for n = 10.5 not possible (since n not integer) oe

(c) 2n2 – 35n + 98 = 0 5

 n   7  4
2× × =
n+7 n+7 9
14n × 9 = 4(n + 7)2
14n × 9 = 4(n2 + 14n +49)
4n2 + 56n + 196 – 126n = 0
 n   7 
M1 for  ×  seen
 n +7   n +7 
 n   7  4
M1 for 2 ×  ×  oe =  
 n +7   n +7  9
st
M1(dep on 1 M) elimination of fractions within an equation
B1 3 terms correct in expansion of (n + 7)2 = n2 + 7n + 7n +
49
A1 full valid completion to printed answer
Edexcel GCSE Maths - Probability of Events (H)

1
(d) 2
9
7 7 7 7
× = × =
n + 7 n + 7 21 21
7 7
M1 for × or better or ft [answer (b)(i)]2
n +7 n +7
2
4  n 
or 1 – –  
9  n +7 
1
A1 for oe cao
9
[13]

10. (a) 0.4

0.6,0.4,
0.6,0.4 2
B1 for LHS: (0.6), 0.4
B1 for RHS: 0.6, 0.4, 0.6, 0.4
(b) 0.36 2
0.6 × 0.6
M1 0.6 × “0.6” [0 < “0.6” < 1]
A1 cao
(c) 38 3
(30 × 42) – (25 × 42.8) = 1260 – 1070 = 190
190 ÷ 5 =
M1 for (30 × 42) – (25 × 42.8) or 1260 – 1070 or 190 seen
M1(dep) for “190” ÷ 5
A1 cao 38
[7]
Edexcel GCSE Maths - Probability of Events (H)

30
11. (a) 1
100
B1 cao
(b) 175 2
250 × 0.7
M1 for 250 × 0.7
A1 cao
175
NB gets M1 A0, 175 out of 250 gets M1 A1
250
[3]

12. (a) 0.495 3

0.55 × 0.45 × 2
M1 for 0.55 × 0.45 or 0.55 × 0.3 or 0.55 × 0.15 seen
M1 (dep) for 0.55 × 0.45 × 2 or adding 3 or 4
correct terms out of 0.55 × 0.3 × 2 +0.55 × 0.15 ×2
A1 cao
(b) 0.255 3
WL or LW or DD
0.55 × 0.15, 0.15 × 0.55, 0.3 × 0.3
0.165 + 0.09
M1 for 0.55 × 0.15 or 0.3 × 0.3
M1(dep) for adding 2 or 3 correct terms
A1cao
[6]

1
13. on LH branch
4
2 1 2
& & on RH branches 2
3 3 3
B1
B1
[2]
Edexcel GCSE Maths - Probability of Events (H)

1
14. (a) on LH branch
4
2 1 2
& & on RH branches 2
3 3 3
B1 cao
B1

7
(b) 3
12
3 2 1 1 6 1
× + × = +
4 3 4 3 12 12
3 2 1 1
M1 for × or × from their
4 3 4 3
tree diagram
M1 for sum of two products
7
A1 for oe
12

(c) 14 3
1 1
n = 21 × 4 or : oe
6 4
1 2
× 84 or 21 ×
6 3
1 3  1 2 1  1
M1 for either ×  =  or ×  =  from their tree
3 4  4 3 4  6
diagram
21
M1 for 21 × 4 (= 84) or ×2
3
A1 for 14 cao
SC: B2 for 63 seen in fraction or ratio
[8]
Edexcel GCSE Maths - Probability of Events (H)

8
15. (a) 3
25
2 3 2 1 8
P(win) = × + × (= )
5 5 5 5 25
2 3 2 1
M1 for × or × or for clearly identifying in P(R) ×
5 5 5 5
P(R) + P(B) × P(B)
" " " " " " " "
2 3 2 1
M1 for P(win) = × + ×
5 5 5 5
8
A1 for , oe
25

(b) £4 2
8
× 100 (= 32)
25
100 × 20 – “32” × 50
"
8"
M1 for ( × 100) × 50 or × 0.5
25
A1 cao
[5]

2 5 2 5
16. , , , 2
5 7 7 7
2
B1 for in the correct place
5
5 2 5
B1 for , , all in the correct place
7 7 7
[2]

2 5 2 5
17. (a) , , , 2
5 7 7 7
2
B1 for in the correct place
5
5 2 5
B1 for , , all in the correct places
7 7 7
Edexcel GCSE Maths - Probability of Events (H)

3 5 2 2
(b) × + ×
5 7 5 7
19
3
35
3 5   2 2 
M1 for  ×' '  or ' ' ×' ' 
 5 7   5 7 
3 5   2 2 
M1 (dep) for  ×' '  + ' ' ×' ' 
5 7   5 7 
A1 cao
[5]

18. (a) (19x + 28)(x – 8)

x=8
x = –28/19 3
M1 for either (ax + b) (cx + d) with ac = 19 and bd = ±224
– b ± b 2 – 4ac
or for a clear attempt to use with a = 19,
2a
b = ±124, c = ±224
124 ± 32400
A1 for either (19x + 28)(x – 8) or for x =
38
A1 for 8 and –28/19 oe (accept –1.47 or better)

(b) red = n blue = n + 2 white = n + (n + 2)

n + (n + 2) + [n + (n + 2)] = 4n + 4 = 4(n + 1)*
Proof 1
B1 for n + (n +2) + [n +(n +2)]
Edexcel GCSE Maths - Probability of Events (H)

 n   n  14
(c)   × 1 – =
 4(n + 1)   4(n + 1)  81
 n   3n + 4  14
  ×   =
 4(n + 1)   4(n + 1)  81
81n(3n + 4) = 14 × 16(n + 1)2
243n2 + 324n = 224(n2 + 2n + 1)
243n2 + 324n = 224n2 + 448n + 224
⇒ 19n2 – 124n – 224 = 0*
Proof 5
M1 for multiplying two fractions
 n   n 
A1for   ×  1 –  oe
 4(n + 1)   4(n + 1) 
B1 for correct expansion of (n + 1)2
M1 for a valid method to eliminate fractions from an algebraic
expression
A1 complete proof

(d) from (a) n = 8 so 4(n + 1) = 36

Proof 1
B1 for substituting n = ‘8’ into 4(n + 1) or 8, 10, 18 seen
Edexcel GCSE Maths - Probability of Events (H)

(e) P(different colours) = 1 – [P(RR)+P(BB)+P(WW)]

8 8 10 10 18 18 
 36 × 36 + 36 × 36 + 36 × 36 
 
OR
P(different colours) = 2 × [P(RB)+P(RW)+P(BW)]
 8 10 8 18 10 18 
=2 ×  × + × + × 
 36 36 36 36 36 36 
OR
P(different colours) =P(RR’)+P(BB’)+P(WW’)
 8 28 10 26 18 18 
= × + × + × 
 36 36 36 36 36 36 
101
3
162
M1 for [P(RR)+P(WW)+P(BB)]
or [P(RB)+P(RW)+P(BW)]
or [P(RR’)+P(BB’)+P(WW’)]
Allow algebraic fractions
M1 (dep) for 1 –[P(RR)+P(WW)+P(BB)]
or 2×[P(RB)+P(RW)+P(BW)]
or P(R)×[1–P(R)]+P(B)×[1–P(B)]+P(W)×[1–P(W)]
Numerical values required
101
A1 cao for oe or 0.62(3...)
162
202
SC B2 for oe or 0.65(1...)
315
[13]

1
19.
4
2 1 2
2
3 3 3
1
B1 for correct on tennis
4
2 1 2
B1 for , , correct on snooker
3 3 3
[2]
Edexcel GCSE Maths - Probability of Events (H)

1
20. (a)
4
2 1 2
2
3 3 3
1
B1 for correct on tennis
4
2 1 2
B1 for , , correct on snooker
3 3 3

3 1
(b) ×
4 3
1
2
4
3 1
M1 for ×
4 3
1
A1 for oe
4

3 2 1 1
(c) × + ×
4 3 4 3
1 1
+
2 12
7
3
12
3 2  1 1
M1 for ×"  " or "  " ×"  "
4 3 4 3
3 2  1 1
M1 ×"  " + "  " ×"  "
4 3 4 3
7
A1 for oe (0.58…)
12
Or
3 1 1 2
M2 for 1 –  × + × 
4 3 4 3
7
A1 for oe (0.58…)
12
[7]
Edexcel GCSE Maths - Probability of Events (H)

21. (a) 0.6 2

0.6, 0.4, 0.6
B1 for LHS: (0.4), 0.6
B1 for RHS: (0.4), 0.6, 0.4, 0.6

(b) 0.4 × 0.4 = 0.16 2

4 4
M1 for 0.4 × 0.4 or × oe
10 10
4 16
A1 for 0.16 or or oe
25 100
[4]

22. 0.62 × 0.38 or 0.2356 4

× 2 oe
= 0.4712
B1 for 0.38 seen
M1 for 0.62 × (1 – 0.62) or 0.2356
M1 (dep) for × 2 oe
A1 for 0.47, 0.471, 0.4712 oe
[4]

23. (a) 0.6 and 0.7, 0.3, 0.7 2

B1 for 0.6 on LH branch
B1 for 0.7, 0.3 and 0.7 on RH branches
(b) 0.4 × 0.3 = 0.12 2
M1 for 0.4 × 0.3
A1 0.12 oe

(c) 0.4 × 0.7 + 0.6 × 0.3 = 0.46 3

M1 for ‘0.4 × 0.7’ or ‘0.6 × 0.3’
M1 for addition of two products from correct branches
A1 0.46 oe
Alternative
M2 for an attempt to evaluate 1 – (0.3 × 0.4 +’0.6 × 0.7’)
A1 cao
[7]
Edexcel GCSE Maths - Probability of Events (H)

4 4 3 3 3 4
24. × × + × ×
7 7 7 7 7 7
48 + 36 84
= =
343 343
But there are three ways this can be achieved:
BBG, BGB, GBB
84
So the probability is ×3
343

64 27
or 1 – –
343 343
NB: 84/343 = 0.244897; 252/343 = 0.73469
4 3
= 0.57(142...), = 0.42(857...)
7 7
252
= 3
343
3 3
4 4 3 3 3 4 4 3
M1 for × × or × × oe or   oe or  
7 7 7 7 7 7 7  7 
oe
91
or or 0.10(49…) or 0.13(99….)
343
M1 (indep) for identification of all 6 outcomes
 4  3  3  3 
(M2 for 1 –   +    ) oe
 7   7  
252 36
A1 , , 0.73(469…) oe
343 49
[3]

25. (a) 0.2

0.58, 0.22 0.2 2
B1 0.2 on jazz on 1st set
B1 0.58, 0.22 0.2
repeated 3 times
(b) 0.2 × 0.2 = 0.04 2
M1 ‘0.2’ × ‘0.2’
A1 cao
Edexcel GCSE Maths - Probability of Events (H)

(c) 0.8 × 0.2 × 2 + 0.2 × 0.2

or
1 – 0.8 × 0.8 = 0.36 3
M1 (0.58+0.22) × ‘0.2’
M1 (0.58 + 0.22) × ‘0.2’ × 2 + ‘0.2’ × ‘0.2’
A1 0. 36 cao
or
M2 1 – (0.58 + 0.22)2
A1 0.36 cao
Listing the outcomes for (c)
CJ 0.58 × ‘0.2’ = 0. 116 FJ 0.22 × ‘0.2’ = 0.044
JC ‘0.2’× 0.58 = 0.116 JF ‘0.2’ × 0.22 = 0.044
JJ ‘0.2’ × ‘0.2’ = 0.04
M2 for all 5 terms added
(M1 for any 2, 3 or 4 terms added)
[7]

26. (a) 0.2 and 0.4, 0.4 2

B1 for 0.2 oe on LH branch
B1 for 0.4 oe on both RH branches

(b) 0.8 × 0.6

0.48 2
M1 for 0.8 × 0.6 oe
A1 for 0.48 oe

(c) 0.8 × 0.4 + 0.2 × 0.6

0.44 3
M1 for 0.8 × ‘0.4’ or ‘0.2’ × 0.6 oe
M1 for 0.8 × '0.4’ + '0.2’ × 0.6 oe
A1 for 0.44 oe
OR
M1 for ‘0.2’ × ‘0.4’ oe
M1 for 1 – (‘0.8 × 0.6’ + ‘0.2’ × ‘0.4’) oe
A1 for 0.44 oe
[7]
Edexcel GCSE Maths - Probability of Events (H)

5
27. (a)
8

5 3 5
, , 2
8 8 8
5
B1 for correct for 1st counter
8
5 3 5
B1 for , , correct for 2nd counter
8 8 8

3 3
(b) ×
8 8
9
oe 2
64
3 3
M1 for ×
8 8
9
A1 for oe
64
[4]

28. (a) Correct diagram 2

B1 for 0.2 oe seen on bottom left branc
B1 for correct probabilities on other branches

(b) prob(WW) = 0.5 × 0.5

0.25 2
M1for 0.5 × ‘0.5’
A1ft for 0.25 oe
[4]
Edexcel GCSE Maths - Probability of Events (H)

5 7 5 8 7 5 7 8 8 5 8 7
29. × + × + × + × + × + ×
20 19 20 19 20 19 20 20 20 19 20 19
or
 5 15 7 13 8 12 
 × + × + × 
 20 19 20 19 20 19 
or
 5 4 7 6 8 7
1–  × + × + × 
 20 19 20 19 20 19 
131
4
190
a b
M1 for at least one product of the form ×
20 19
M1 for identifying all products
(condone 2 errors in 6 products, 1 error in 3 products)
Either
 5 7 5 8 7 5 7 8 8 5 8 7 
 × , × , × , × , × , × 
 20 19 20 19 20 19 20 19 20 19 20 19 
or
 5 15 7 13 8 12 
 × , × , ×  or
 20 19 20 19 20 19 
 5 4 7 6 8 7 
 × , × , × 
 20 19 20 19 20 19 
M1 (dep) for
 5 7 5 8 7 5 7 8 8 5 8 7 
' × + × + × + × + × + × '
 20 19 20 19 20 19 20 19 20 19 20 19 
oe
 5 15 7 13 8 12 
or  ' × + × + × '  oe
 20 19 20 19 20 19 
 5 4 7 6 8 7 
or 1 –  ' × + × + × '  oe
 20 19 20 19 20 19 
131
A1 for oe or 0.68947… correct to at least 2 decimal places or
190
answer that rounds to 0.69
NB : If decimals used for products then must be correct to at
least 2 decimal places
Edexcel GCSE Maths - Probability of Events (H)

With replacement
M0
M1 for identifying all products
(condone 2 errors in 6 products, 1 error in 3 products)
either
 5 7 5 8 7 5 7 8 8 5 8 7 
 × , × , × , × , × , ×  or
 20 20 20 20 20 20 20 20 20 20 20 20 
 5 5 7 7 8 8 
 × , × , ×  or
 20 20 20 20 20 20 
 5 15 7 13 8 12 
 × , × , × 
 20 20 20 20 20 20 
M1 (dep) for
 5 7 5 8 7 5 7 8 8 5 8 7 
' × + × + × + × + × + × '
 20 20 20 20 20 20 20 20 20 20 20 20 
 5 15 7 13 8 12 
or  ' × + × + × '
 20 20 20 20 20 20 
 5 5 7 7 8 8 
or 1 –  ' × + × + × '
 20 20 20 20 20 20 
262 262
A0 for oe or 0.655 (NB: oe or 0.655 implies M2)
400 400
Partial replacement
141 121
SC: B2 for oe or 0.705 or oe or 0.6368… correct to
200 190
at least 2 decimal places
[4]

30. (a) 0.8,

0.4, 0.6, 0.4 2
B1 for Julie correct
B1 for Pat correct
(b) 0.12 oe 2
0.2 × 0.6
M1 for 0.2 × 0.6
A1 cao
[4]
Edexcel GCSE Maths - Probability of Events (H)

31. (a) 0.7, 0.7, 0.3, 0.7 2

B1 for Monday correct
B1 for Tuesday correct
(b) 0.51 oe 3
1 − 0.7 × 0.7
M1 for 0.7 × 0.7
M1 for 1 − “0.49”
A1 for 0.51 oe
(M1 for 0. 3 × 0. 3 OR 0.7 × 0.3 OR 0.3 × 0.7
M1 for 0. 3 × 0. 3 + 0.7 × 0. 3 + 0. 3 × 0.7
A1 for 0.51 oe)
[5]

660
32. oe 5
1000
Total = 3 + 5 + 2 (= 10)
3 3 5  45  3 3 2  18 
× × = , × ×  = 
10 10 10  1000  10 10 10  1000 
5 5 3  75  5 5 2  50 
× × = , × ×  = 
10 10 10  1000  10 10 10  1000 
2 2 3  12  2 2 5  20 
× × = , × ×  = 
10 10 10  1000  10 10 10  1000 
 "45" "18" "75" "50" "12" "20" 
3×  + + + + + 
 1000 1000 1000 1000 1000 1000 
660
1000
M3 for all six expressions seen OR their combined equivalents
(M2 for four expressions seen OR their combined equivalents)
(M1 for two expressions seen OR their combined equivalents)
M1 sum of 18 relevant products condone 1 slip
660
A1 for oe
1000
SC: without replacement maximum M4 A0
38 28
SC: Just 2 beads: Answer either oe OR oe B1
100 90
[5]
Edexcel GCSE Maths - Probability of Events (H)

33. (a) 42g

8 3
Median at 50.5 (50)
100 − 92
B1 for 42g to 43g
1
M1 for reading correctly from graph ± sq and
2
subtracting from 100
A1 for 7, 8 or 9
(b) cf 2
1
B1 for plots (condone one error) ± sq
2
B1 (dep) for joining points to give cf graph
SC: B1 if points plotted consistenly within intervals
(condone one error) and joined
(c) 0.0128 4
100 − 84 = 16
0.16
0.08 × 0.16
"8"
B1 for oe (Tawny Beach)
100
15 16 17
B1 for or or oe (Golden Beach)
100 100 100
M1 for multiplying two probabilities
A1 ft (dep on B2)
[9]

4
34. oe 4
9
2 1 1 2
× + ×
3 3 3 3
2 1
B1 for or seen
3 3
M1 for multiplying their P(H) by their P(T),
P(H) ≠ P(T), 0< probs. < 1
M1 (dep) for × 2
4
A1 for oe OR 0.4 or 0.444(4…) no errors seen
9
[4]
Edexcel GCSE Maths - Probability of Events (H)

35. (a) 5 fractions 2

4 1 3 1 3
and , , ,
7 4 4 4 4
B1 for bag P correct
B1 for bag Q correct

3
(b) oe 2
28
3 1
×
7 4
3 1
M1 for ×” “(0 < 2nd fraction < 1)
7 4
A1
[4]

36. £67.50 4
Paid in = 150 × £1.20 (= 180)
No. of winners =
3
× 150(= 45)
10
Profit = “180” – “45” × 2.50
B1 for 150 × 1.20 (= 180)
3 7
M1 for × “150” (= 45) or × “150”(= 105) or 54
10 10
M1 for “180” – “45” × 2.50 (= 180 – 112.50)
A1 for £67.50, £67, £68
Alternative method
B1 for 2.50 – 1.20 (= 1.30)
3 7
M1 for × “150” (= 45) or × “150”
10 10
M1 for “105” × 1.20 – “45” × “1.30”
A1 for £67.50, £67, £68
Alternative method
B1 for 0.3n × 2.50
M1 for 1.20n
150
M1 for (1.20n – 0.3n × 2.50) ×
n
A1 for £67.50, £67, £68
[4]
Edexcel GCSE Maths - Probability of Events (H)

37. 14 3
1 1
n = 21 × 4 or :
4 6
1 2
× 84 or 21 ×
6 3
1 3 1 2 1 1
M1 for ×  =  or ×  = 
3 4 4 3 4 6
21
M1 for 21 × 4 = 84 or ×2
3
A1 cao
[SC:B2 for answer of 63]
[3]

38. (a) 0.6

0.3 0.4
0.6 2
B1 for 0.3
B1 for 0.6, 0.4, 0.6

(b) (0.7 × 0.6) + (0.3 × 0.4)

0.54oe 3
M1 for either 0.7 × “0.6” or “0.3” × “0.4”
M1(dep) for (0.7 × “0.6”) + (“0.3” × “0.4”)
A1 cao
[5]

39. (0.7 × 0.2) + (0.8 × 0.3) = 0.14 + 0.24

0.38 oe 3
M1 for either 0.7 × 0.2 or 0.8 × 0.3
M1 for 0.7 × 0.2 + 0.8 × 0.3
A1 cao
SC: If no marks earned then B1 for fully correct tree diagram
with probabilities shown
[3]
Edexcel GCSE Maths - Probability of Events (H)

40. (a) 1 – (0.3 + 0.25) 2

= 0.45 oe
M1 for 1 – (0.3 + 0.25)
A1 for 0.45 oe
oe meaning that the probability must be given alternatively as a
fraction (45/100 or an equivalent fraction), or as a decimal
(45%).
Ratios, words (eg 45 to 100) get A0, could get M1 if working
shown.
NB the decimal is not always clear; use working to clarify its
existence if necessary, by 045 on the answer line without other
working to substantiate should get 0 marks. Accept a comma for
the decimal.

(b) 0.3 × 200 2

= 60 or “60 out of 200”
M1 for 0.3 × 200, or for sight of the number 60 on the answer
line (eg in 60/200).
A1 cao
[4]

41. 1 – P(2 greens) 3

5 4
=1 – ×
9 8
20
=1 –
72
52
= oe
72
M1 for p(2nd stone) being a fraction with a denominator of 8
5 4
M1 for 1 – × oe or the sum of any 2 of:
9 8
4 3 4 5 5 4
× , × , × (ignore the sum of additional products)
9 8 9 8 9 8
52
A1 for oe [0.722…]
72
5 5
[SC: if no marks awarded, B1 for 1 – × oe]
9 9
OR if using a sample space approach:
M1 for correct table
M1 for correct identification of all the cases
52
A1 for oe [0.722…]
72
[3]
Edexcel GCSE Maths - Probability of Events (H)

42. 1 – 0.6 – 0.3 2

= 0.1
M1 for 1 – (0.6 + 0.3) oe
A1 cao
[2]

43. (a) 7/10 2/9, 7/9 3/9, 6/9 2

B2 for all 5 correct
(B1 for 2, 3, or 4 correct)

42
(b) 2
90
M1 for “1st girl” × “2nd girl”
A1 cao.
[4]

2 1 3 1
44. × × × 4
5 6 5 2
11
= oe
30
3 1
M1 for or seen
5 6
(could be part of a calculation)
2 1 3 1
M1 indep for × oe or × oe
5 6 5 2
2 1 3 1
M1 for × + ×
5 6 5 2
11
A1 for oe
30
[4]

45. 4/7
5/11, 6/11, 5/11 2
B2 for all four probabilities correct
(B1for 1 probability correct)
[2]
Edexcel GCSE Maths - Probability of Events (H)

 3 2  2 1  4 3
46.  × + × + × 
9 8 9 8 9 8
6 + 2 + 12
=
72
20
4
72
2 1 3
B1 for or or seen as 2nd probability
8 8 8
3 2 2 1 4 3
M1 for  ×  or  ×  or  × 
9 8 9 8 9 8
3 2 2 1 4 3
M1 for  ×  +  ×  +  × 
9 8 9 8 9 8
20
A1 for o.e.
72
Alternative scheme for replacement
3 2 4
B0 for or or seen as 2nd probability
9 9 9
3 3 2 2 4 4
M1 for  ×  or  ×  or  × 
9 9 9 9 9 9
3 3 2 2 4 4
M1 for  ×  +  ×  +  × 
9 9 9 9 9 9
29
A0 for
81
Special cases
29 20 29
S.C award B2 for or or
81 81 72
2 1 3 3 2 4
SC award B1 for and and or and and seen as
9 9 9 8 8 8
second probability if B2 not scored
Watch for candidates who misread the question and work with
10ths and 9ths They can score M2
Any other total for the number of yoghurts must be identified
before ft
[4]

47. (a) 1 – (0.2 + 0.35 + 0.2)

0.25 2
M1 for 1 – (0.2 + 0.35 + 0.2)
A1 0.25 oe
SC: B1 for “1 out of 4” or “1 in 4”
SC: B1 if 0.25 seen in the table with incorrect answer on
answer line.
Edexcel GCSE Maths - Probability of Events (H)

(b) 100 × 0.35

35 2
M1 for 100 × 0.35
A1 cao
[4]

3 2
48. ×
8 7
6
3
56
2
M1 for seen as non-replacement
7
3 2 3 3 3 2 3 3
M1 for × , × , × , × oe seen
8 7 8 8 8 8 8 7
6
A1 for o.e.
56
[3]

49. Reason 1
B1 for indication of not enough trials
[1]

50. (a) 4/5

(7/10, 3/10) (1/10, 9/10) 2
B2 cao
(B1 for 2 correct from 4/5, (7/10, 3/10), (1/10, 9/10))

(b) (1/5 × 7/10) + (4/5 × 1/10)

11/50 3
M1 for 1/5 × “7/10” or “4/5” × “1/10” oe selected
M1 for (1/5 × 7/10) + (4/5 × 1/10) oe
A1 for 11/50 oe
[5]
Edexcel GCSE Maths - Probability of Events (H)

5 7 5 1 3 2 3 1 2 2 2 7
51.  × + × + × + × + × + × 
 10 10   10 10   10 10   10 10   10 10   10 10 
35 + 5 + 6 + 3 + 4 + 14
=
100
OR
 5 2   3 7   2 1 
1 –  ×  +  ×  +  × 
 10 10   10 10   10 10 
10 + 21 + 2 33
=1– = 1−
100 100
67
4
100
M1 for a tree diagram with at most 2 errors
 5 7   5 1 
or one of  ×  or  ×  etc
 10 10   10 10 
M1 for 5 out of 6 correct pairings of different colours
or 2 out of 3 correct pairings of same colours
or 8 out of 9 correct pairings of all colours
M1 (dep on M2) for adding 5 or 6 correct pairings of different
colours
or 1 – (2 or 3 correct pairings of same colours)
67
A1 for oe
100
x
SC All correctly done but 2nd spinner all
9
Award M1 for a “correct tree”
M1 for adding 5 or 6 “correct pairings” of different colours or
1 – (2 or 3 “correct pairings” of same colours)
M0 A0 (answer = 67/90)
[4]
Edexcel GCSE Maths - Probability of Events (H)

 4 3   3 2   2 1  12 + 6 + 2
52.  × + × + ×  =
9 8 9 8 9 8 72
20
oe 4
72
3 2 1
B1 for or or seen as 2nd probability
8 8 8
4 3 3 2 2 1
M1 for  ×  or  ×  or  × 
9 8 9 8 9 8
4 3 3 2 2 1
M1 for  ×  +  ×  +  × 
9 8 9 8 9 8
20
A1 for oe
72
Alternative scheme for replacement
4 3 2
B0 for or or seen as 2nd probability
9 9 9
4 4 3 3 2 2
M1 for  ×  or  ×  or  × 
9 9 9 9 9 9
4 4 3 3 2 2
M1 for  ×  +  ×  +  × 
9 9 9 9 9 9
29
A0 for
81
Special cases
29 20 29
S.C. if M0 scored, award B2 for or or
81 81 72
3 2 1
S.C. if M0 scored award B1 for or or
9 9 9
3 2 4
or and and as second probability if B2 not scored
8 8 8
[4]

01. Mathematics A Paper 4

Part (a) was answered well by candidates of all abilities. Acceptable explanations often
5
mentioned 100 as the expected number of sixes. The first mark in part (b) for writing on the
6
“Not Six” branch was gained by many candidates but the tree diagram was often not completed
correctly. Candidates commonly forgot labels, gave incorrect probabilities, or added only one
more branch to the diagram.
Edexcel GCSE Maths - Probability of Events (H)

Mathematics B Paper 17
Candidates of all abilities managed to gain credit in part (a) for a reasonable explanation of the
problem. This was well answered. Candidates who failed to score usually offered a
contradictory explanation.
A completely correct tree diagram in part (b) was rare. Most attempts had one branch only from
each of the two given branches. 5/6 was often seen as the probability for the red dice not
showing a six, and this was often the only mark gained.

02. Some of the most able candidates presented precise elegant solutions within a few lines of
working. The vast majority of the non-A* candidates drew a tree diagram and proceeded to
calculate the probabilities of all the possible combinations. Those who showed the results as
double products of fractions generally scored more than half the marks for the question but
those who evaluated without any evidence generally scored poorly. Many candidates did not go
on to add the 18 relevant probabilities from their tree diagram. A high proportion of those who
did attempt the correct sum made arithmetical errors.

03. Part (a) required candidates to comment on a statement about a probability. Most thought that
the dice was unfair, maintaining that they would have expected 100 sixes. A few used the
phrase ‘about 100 sixes’. Some did say that the dice was fair, because it is possible to get 200
out of 600 sixes from a fair dice.
Part (b) required candidates to complete a probability tree diagram. Most did so by drawing two
more sets of two branches, correctly labelling and getting full marks. A few candidates thought
that they should just draw 2 out of 4 branches. A few candidates drew the 4 branches but the
probabilities on pairs of branches did not add up to 1.
Part (c) was a standard task and was well done by many candidates. The main error of good
candidates was in (ii) where they interpreted the task as finding exactly one six. However, there
were a sizeable number who thought that
1 × 1 = 2 when multiplying the fractions together.

04. Many candidates did not realise that the numerical values given in the stem of the question had
some relevance to the answer! Many candidates tried to argue that they may be dependent or not
depending on whether they came to school together or not.
Some candidates did realise that for events to be independent Prob (both A and B) = Prob (A) ×
Prob (B) and were able to use the given information to come to the correct conclusion.

05. In part (a), most candidates applied a correct method but some left the answer as 7.4 or
incorrectly rounded to 7. In part (b), a common wrong answer was 90. The final part of the
question was answered well although some candidates failed to appreciate the need for a
7
product and just gave the answer as .
18
Edexcel GCSE Maths - Probability of Events (H)

06. This was a complex probability question, involving either the use of the complementary event
or a combination of 6 mutually exclusive events. Many candidates were able to sort out the
correct combinations and then add the respective probabilities.

07. This was truly a question of “two halves”. Part (a) was well answered. Nearly all candidates
correctly gave the 0.4 on the left hand branch, and the majority went on to gain the second
mark, but is was disappointing to find many errors on the right hand side, including careless
reversals of the 0.6 and 0.4, or an apparent desire to make all four probabilities sum to 1. In Part
(b) few gained any marks; there was little understanding of what the calculation of the mean
involves.

08. Mathematics A Paper 5

The common error was to multiply the two probabilities.

Mathematics B Paper 18
Candidates were generally less successful with many multiplying the probabilities rather than
adding them.

09. Mathematics A Paper 5

Although full correct solutions for this question were seen by the best candidates it was a rarity.
Except for answers to (b)(i) it was unusual to find candidates at grade C and low B gain any
further credit although some high grade B candidates scored 4 or 5 marks normally in parts (a)
and (b). In part (a) those who applied a systematic approach were generally far more successful
as illustrated by “2 × 98; 4 × 49; 28 × 7**” In part (b)(i) many of the given expressions were
n
correct although was a common wrong answer. In part (b)(ii), although many could not
n+7
present an adequate proof/explanation with a common wrong approach based on the ‘fact’ that
“Bill is saying that there is only a total of 5 balls and we have 7 white balls”, it was pleasing to
find even some grade B candidates presenting a full logical proof based on n=10.5 and unable to
have half a ball. Part (c) was very poorly answered with most just attempting to solve the
equation (again). Of the reasonable attempts most gained credit for one product of two
probabilities and a correct expansion of (x 7)2 but many failed to eliminate the algebraic
fractions correctly or missed out the second combination of probabilities. It was pleasing to find
candidates recovering in the last part to gain a method mark for a relevant squaring of their
answer to part (b)(i).
Edexcel GCSE Maths - Probability of Events (H)

Mathematics B Paper 18
In part (a), the majority of candidates were unable to factorise the given expression. Of those
who did obtain the correct factorisation a number then went onto solve the associated equation
7
incorrectly with 7 (instead of ) being a popular incorrect solution. The majority of candidates
2
were able to give the correct probability in part (bi) but then in (bii) were unable to offer a
convincing proof that Bill’s statement could not be correct. Part (c) was very poorly done with
the majority of candidates starting with the equation given rather than using the information
given to derive it. In part (d) very few candidates referred back to the expression for the
probability quoted in (bi).

10. Mathematics A Paper 6

Parts (a) and (b) were well answered. There were a few candidates who thought the question
was about sampling without replacement.
Part (c) proved to be more of a challenge, with many candidates failing to appreciate that the
key idea involved find the total time for the original 30 CDs and subtracting the total time for
the 5 CDs.

Mathematics B
Paper 17
All but a minority gained one mark in part (a), usually for a correct probability on the first
branch of the tree diagram.
In part (b) only very few were able to gain any marks, usually 3 or nothing.
Paper 19
Part (a) was well done although some candidates did write the product of two probabilities for
the second choice rather than the probability. The majority of candidates successfully answered
part (b). A common error here was to add rather than multiply the two probabilities. Part (c) was
very poorly done with the majority of candidates having no real idea how to tackle the question.
The common incorrect approach was to calculate the difference between the mean playing times
and subtract this from the mean playing time of all the CDs.
Edexcel GCSE Maths - Probability of Events (H)

11. Paper 4
Overall this question was well answered, with over half the candidates gaining full marks. In
part (a) a minority of candidates failed to give the correct answer. Their errors included writing
the probability using incorrect notation, giving 1/6, or just “30”. Surprisingly a greater
proportion of candidates gave the correct answer in part (b). The only significant errors in this
part were the writing of the answer as a probability (eg 175/250) rather than a simple number, or
performing a division: 25 ÷ 7.
Paper 6
Part (a) involves using the table to give an estimate of a probability.
Part (b) asked candidates to estimate the number of cases out of 250 based on a probability of
0.7. Virtually all candidates at this tier were able to do this. A few left the answer as a fraction
with a denominator of 250.

12. This was an unstructured probability question. In the first part candidates had to realise that they
had to use the probability of a ‘not win’ to get 0.55 × 0.45. This then has to be multiplied by 2
and evaluated. Some candidates drew a tree diagram and were able to add together 4 terms to
get the correct answer of 0.495.
In the second part, candidates had to realise that there were three possible cases to consider.
These were ‘win, lose’, ‘lose, win’ and ‘draw, draw’ over the two games. Many candidates were
able to identify at least one of these terms but the overall success rate was not high.
Weaker candidates assumed that all possible cases were equally likely.

13. Specification A
A well answered question. The only common error was to use quarters on the right hand
branches.
Specification B
¼ was often seen in the first pair of branches, gaining one mark, however there were many
confused attempts at completing the second pairs of branches, often still using quarters.

14. Part (a) was generally done well.

In part (b), many candidates knew that they had to multiply and then add the probabilities, but
1 1 2
only about half were able to do this accurately. A common error was × = .
4 3 12
Candidates generally found part (c) of this question difficult. Only the best candidates were able
to achieve all the mark, though there were many that achieved at least one mark- usually for
3 1
writing × . Common answers were 63 and 84- which were awarded two marks.
4 3
Edexcel GCSE Maths - Probability of Events (H)

15. Many candidates had a good idea of how to deal with the task in part (a). Some drew probability
tree diagrams and were able to select the appropriate routes through the branches. Others simply
wrote down the correct pair of products. The addition of the fractions was carried out well and
1 2 3
the correct answer often seen. A very common error was to work out × as . A common
5 5 25
misread was to assume that the colours on the two dice were the same – red, blue and green.
Part (b) was generally well answered. Most candidates realised that they had to work out the
total income from 100 × 20p and then the expected payout from expected number of winners ×
50p. A few candidates got confused and multiplied by 30p instead of 50p.

16. This question was usually well answered. Common misunderstandings included a reversal of
the 2/7 and 5/7 on the bottom two branches, or a failure to use 7 in the denominator.

17. Most candidates inserted the correct fractions into the probability tree diagram. Part (b) was also
19
well answered with the correct answer of often seen. Common occurring errors included a
35
correct method, but with the multiplication carried out wrongly by making the denominators of
the fractions the same, followed by incorrect multiplication. A few candidates thought that they
had to add the fractions. They scored no marks.

18. Some weaker candidates gained marks in (a) and (b). In part (a), strong candidates gained a
mark for substituting the values of a, b and c into the quadratic formula- those quoting the
formula with greater success than those who didn’t. The negative values of b and c proved a
hurdle to many in their evaluation of b2 –4ac.
Part (b) was done well by the majority of candidates.
In part (c), only the best candidates gained any credit, usually for writing
n 3n + 4 14
× = . Those that went on to eliminate the fraction generally managed to
4(n + 1) 4(n + 1) 81
complete the proof without error. Candidates that solved part (a) correctly usually gained the
mark for part (d). A significant number of candidates solved 4 ( n+ 1)=36 to get n = 8, but did
not then relate this to part (a). A few recovered by listing 8, 10 and 18.
In part (e), an encouraging number of candidates could add the product of three fractions,
usually P(RB), P(RW) and P(RW) which were often derived from a tree diagram. Final answers
were usually given as a fraction.

19. Specification A
The tree diagram was completed correctly by more than half of the candidates. It was not
surprising that most errors were made on the bottom two right hand branches.
Edexcel GCSE Maths - Probability of Events (H)

Specification B
1
Most candidates scored at least one mark here, usually for correctly labelling the in the first
4
branch. Failure in the second branches often arose from including quarters in one or more of the
probabilities.

20. Specification A
The probability tree diagram was generally completed correctly. Part (b) was almost always
3 1 4
answered using a correct method although there were the occasional errors of × = .
4 3 12
Answers to part (c) were also good, but less successful than part (b). There were the usual errors
of confusing the use of multiplication and addition in the method as well as the accuracy errors
of the type outlined for part (b).

Specification B
The tree diagram in part (a) was completed correctly by over 90% of candidates. Parts (b) and
(c) were generally well answered although more candidates than usual attempted to add rather
than multiply the relevant probabilities. A few candidates indicated that they knew that the
relevant probabilities in (a) needed to be multiplied but then went on to add them regardless.

21. The majority of candidates were able to complete the tree diagram in part (a). In part (b), most
candidates knew that they were required to multiply 0.4 by 0.4 but a large proportion of these
had problems in doing this- typically giving their answer as 1.6 or 0.8. Relatively few added the
probabilities.

22. Most competent candidates drew a tree diagram and were able to identity the correct branches
and carry out the appropriate calculations. A few candidates forgot that there were two possible
ways in which the required outcome could happen and so only gained half marks.
Edexcel GCSE Maths - Probability of Events (H)

23. Part (a) of this question was done well by the majority of candidates, scoring at least one mark
for 0.6 on the first branch.
In parts (b) and (c), candidates often identified the correct probabilities, but a significant number
were confused about that operations they should be using. A popular error was to add the
probabilities along the branches instead of multiplying them. A surprising number of those
candidates who multiplied probabilities were unable to do this correctly, e.g. 0.3 × 0.4 was often
evaluated as 1.2. In part (c), many candidates worked with the correct two pairs of branches, but
many of these were confused about the order of the operations; a common incorrect method was
(0.6 + 0.7) × (0.6 + 0.3). A popular incorrect answer was 4.6
As the question was written in decimals most candidates kept the probabilities in this form, it
was noted, however, that those candidates who converted their decimals to fractions were often
more accurate with their answers than those that hadn’t.

24. This was a reasonably demanding probability question as candidates had to decide what
approach to take. Many decided to draw a tree diagram and then identify which were the
relevant branches. They tended to be more successful than those who did not draw the
4 3 3 4 4 3
probability tree. Often, those candidates identified the expressions × × and × × but
7 7 7 7 7 3
then acted as if these were the only 2 cases or doubled both probabilities giving a total of 4
cases.
3 3
4 3 252
A few candidates dealt with the complementary event and calculated 1 –   –   = .
7 7 343

25. Part (a) was well answered. Very few candidates thought that this was sampling without
replacement.
Answers to part (b) were split between the correct 0.2 × 0.2 and the incorrect 0.2 + 0.2, although
some candidates evaluated the former as 0.4
Answers to part (c) generally considered some of the 5 cases. Quite often the answer 0.2 was
seen from 0.58 × 0.2 + 0.22 × 0.2 + 0.2 × 0.2 or the answer 0.32 from (0.58 × 0.2 + 0.2) × 2
The approach 1 – P(No jazz) was rarely seen, but usually led to the correct answer.
Edexcel GCSE Maths - Probability of Events (H)

26. Part (a) was done well by the vast majority of the candidates. In part (b), many candidates knew
that they needed to multiply the probabilities but a significant number of these were unable to
do the calculation accurately, e.g. 0.8 × 0.6 = 4.8 or 0.42. Common incorrect methods were 0.8
0.8 + 0.6
+ 0.6 = 1.4 and = 0.7 . In part (c), only the best candidates were able to score full
2
marks for this question, but many were able to score 1 mark for either 0.8 × 0.4 or 0.2 × 0.6.
Common errors here were similar to those in part (b), e.g. those involving poor arithmetic, e.g.
0.8 × 0.4 = 3.2, 0.24 or 2.4, or those involving confusion as to when to multiply the probabilities
or when to add the probabilities, e.g. (0.8 + 0.4) × (0.2 + 0.6).

27. Accurate completion of the probability tree diagram was good with most candidates scoring at
least one mark. In part (b) however a great many candidates added the probabilities instead of
3 3
multiplying. It is also of note that of the candidates who correctly quoted × a significant
8 8
9
number failed to correctly work out this product; being a common error.
16

28. Very few candidates failed to score any marks at all in this question.
Part (a) was answered very well with most candidates completing the probability tree diagram
correctly. Errors usually occurred on the right hand branches where some candidates put the
values 0.5, 0.3 and 0.2 in the wrong order and some inserted the results of multiplying two
probabilities together. A significant number of candidates were not aware that they needed to
multiply the probabilities on the relevant branches in part (b) and many added 0.5 to 0.5 instead.
Even when candidates did write down 0.5 × 0.5 this was sometimes evaluated incorrectly with
answers of 0.5, 1 and even 2.5 seen quite frequently. Some candidates with incorrect answers
lost the opportunity of gaining a method mark here because they did not show any working.

29. A large number of candidates drew tree diagrams, which in most cases were helpful: however
some candidates drew them so big that their calculations were then squashed around the edges
with very little logical flow. Most candidates seemed to have assumed that there was
replacement and so limited themselves to 2 out of the four marks. It was common to consider
only three scenarios instead of 6, for example red then orange but not orange then red. It was
more common to see 6 fractions added rather than 1 – the complement.

30. Part (a) was generally well done. However, a number failed to get the correct entries for Pat.
Part (b) could be done independently of the probability tree diagram. Many candidates wrote
down the correct expression of 0.2 × 0.6 and obtained the answer 0.12. However, a significant
number of candidates gave an answer of 1.2. The incorrect method of 0.2 + 0.6 was frequently
seen.
Edexcel GCSE Maths - Probability of Events (H)

31. Part (a) was well answered. In part (b) the majority of candidates found one product correctly
but few were able to demonstrate a fully correct method often failing to appreciate the
mathematical meaning of ‘at least’. It is disappointing to report that many could not correctly
find the value of the individual products and some final answers were even greater than one.

32. The majority of candidates were able to attempt this question. A few candidates simply drew the
relevant tree diagram and failed to give any probabilities. Of those candidates who did use
probabilities, most were able to score at least 3 of the available 5 marks. Those who did not
score full marks generally failed to recognise that the order that the beads were selected was
important and thus red, red, green had to be included as well as red, green, red and green, red,
red.

33. Parts (a) and (b) were well done by the majority of candidates. In part (c) most candidates were
able to write down the relevant probabilities correctly but these were then frequently added
rather than multiplied. A common arithmetic error in this question was to give the answer to
100 × 100 as 1000.

34. Many good candidates scored some marks in answering this question. Some failed to find the
correct probabilities for heads or tails from the information given but realised that they
probabilities they had found needed to be multiplied. Fewer candidates added the two relevant
probabilities. Greater success came from those candidates who worked entirely in fractions than
decimals. Weaker candidates seemed happy to use probabilities grater than 1.

35. Completion of the tree diagram was well done by the vast majority of candidates. In part (b) a
significant number of candidates added rather than multiplied the probabilities. The main
concern, however, was candidates’ failure to always evaluate the fraction product correctly. It is
worth noting that section B is a calculator section and so the product should not have been a
3 1 4 1
problem. A common error was × = = or, perhaps worse in a probability question,
7 4 28 7
3 1 12 7 84
× = × = =3
7 4 28 28 28

36. This was an unfamiliar type of question for candidates but was one that was generally well
answered. Over 85% of candidates were able to score at least one mark for their solution with
just over 60% of candidates gaining full marks. A common error was for candidates to equate
3 1
to in their calculation.
10 3
Edexcel GCSE Maths - Probability of Events (H)

37. Over 60% of candidates used the probabilities on the tree diagram correctly and indicated that
they would multiply appropriate probabilities. Unfortunately, many arithmetic errors were then
seen; a significant number of candidates added rather than multiplied the probabilities. A
common error was to give the answer as 63 coming from subtracting the number of times both
games were won from the total number of games played.

38. Part (a) was answered correctly by the majority of candidates. Candidates generally had much
less success with part (b) which was poorly done. A significant number of candidates added the
probabilities and then averaged these. Another incorrect method was to find the two correct
products but then multiple these instead of adding them.

39. The unstructured nature of this question made it more demanding for candidates. Many were
able to draw a correct tree diagram and progress to finding the required probability. A number
of candidates added instead of multiplying the appropriate probabilities. The most common
error was either to evaluate the probability of passing both exams or to evaluate the probability
of passing at least one exam.

40. The majority of candidates gained full marks in part (a). A surprising number gave 0.28 as the
sum of 0.3 and 0.25, leading to the answer of 0.72. This was a common error, which is all the
most disappointing since this is a calculator error. Was this an indication of the absence of a
calculator? Or were many candidates trusting to poor arithmetic and not checking their work
with their calculator? Those candidates who did not understand the process of relative
probability performed a division rather than a multiplication in part (b). There were few who
gave their answer as a probability rather than as a quantity. Most gained full marks.

41. It was encouraging to see so many candidates who clearly understood that fractions of 9, then 8
were needed. These were commonly expressed on a probability tree diagram. A small number
attempted to add the probabilities, rather than multiplying. Many calculated the four products,
but then had difficulty in picking those that were needed to answer the question. It is
discouraging to see many failed attempts to cancel fractions, particularly when candidates have
arrived at the correct answer.

42. This question was very well answered with most candidates gaining both marks.
Edexcel GCSE Maths - Probability of Events (H)

43. Candidates clearly understood the concept of a tree diagram and there were many fully correct
answers to this question. A significant minority of candidates however, did not recognise this as
a “non-replacement” situation and marked the same probabilities ( 103 , 107 ) on the second stage of
their diagram. Although these candidates were unable to gain any marks for at least two correct
probabilities in part (a), many used their probabilities correctly in part (b) to gain some credit in
that part of the question. In part (b) some candidates failed to identify the need to multiply two
probabilities and disappointingly, a significant number attempted to add the probabilities,
sometimes giving numbers greater than one as their answers. 13 was often seen following
19
7 + 6 . A number of candidates misread the question and gave the probability of at least one
10 9
girl. Candidates who worked out the correct answer ( 42 ) but failed to simplify their fraction
90
correctly were not penalised as the question was not testing this skill. This does however
confirm the need for candidates to show their method clearly in the space for working. The need
to show working was also highlighted by those candidates who knew they had to multiply, and
wrote this down, but had insufficient ability with fractions to complete this correctly and those
who could not correctly multiply 6 by 7.

44. Over half the candidates were able to access the first mark by showing that not stopping at one
of the lights was 3/5 or 1/6. A further 12% then went on to gain the second mark by showing
3/5 × 1/2 or 2/5 × 1/6. However poor arithmetic let many candidates down with 2/5 × 1/6 = 3/30
commonly seen. Even those candidates who did get to 3/10 + 2/30 then went on to write 5/40.
Some overlooked the different probabilities at the second set of lights and assumed 5/6 and 1/6
on both branches. This led to answers of (2/5 × 1/6) + (3/5 × 5/6) = 17/30. A significant
minority obtained a correct tree and then tried to add probabilities. Yet others seemed to think
that a common denominator was needed when multiplying fractions often introducing
arithmetic errors as a result.

45. This question was well understood but it was surprising to see so many candidates making
errors in labelling the probabilities for snooker. The Darts “Not win” was almost correctly
labelled by 96% of candidates but they often switched the probabilities for “win” and “not win”
for snooker.
Edexcel GCSE Maths - Probability of Events (H)

46. This was a fairly standard, but non-trivial, probability question. Many successful candidates
drew correct probability tree diagrams and used them properly. 24% of candidates knew that
they had to multiply the probabilities together as they worked along a set of branches starting
with the root and were then able to add the resulting 3 fractions correctly to get the right answer.
However, there were a large number of errors due to inability to tackle the arithmetic of
fractions correctly. These were of the following general types:
3 2 5 2 1 3
• carelessness, exemplified by one of × = or × =
9 8 72 9 8 72
3 2 5
• confusion over multiplication, exemplified by all of × = ,
9 8 72
2 1 3 4 3 7
× = and × =
9 8 72 9 8 72
3 2 42 3 2 432
• confusion over multiplication as exemplified by × = or × =
9 8 72 9 8 72
6 2 12 20
• confusion over addition as exemplified by + + =
72 72 72 216

Many candidates made life harder for themselves by calculating the correct fractions for the
cases SS, PP and CC, cancelling them and then making an error on the addition of the three
fractions with different denominators.
Some candidates treated the problem as one of replacement and were rewarded as they had
essentially the correct method.
Some candidates thought the total of yoghurts was 8 rather than 9 and ended up with a fraction
over 56 and there were also some candidates who tried to eat 3 yoghurts.
2 2
Other candidates gave fractions such as prob. (2nd is S) = rather than .
9 8
Some candidates drew out the whole equally likely sample space for the case with replacement
29
and obtained the answer
81
There were, of course many candidates who tried to draw a probability tree but could not get its
structure correct (generally they did not have 3 branches from every node) and many others who
could not get as far as that. 45% of candidates scored no marks.
Edexcel GCSE Maths - Probability of Events (H)

47. This question was well answered. In part (a) the vast majority of candidates (94%) were
successful with only a small minority of weaker candidates extending a perceived number
sequence to give “0.35” as their answer. Other candidates were unable to add probabilities or
subtract their total from one accurately and so did not gain full credit for their answer to this part
of the question. Not quite as many candidates (77%) successfully completed part (b). Some
candidates gave the answer “25” apparently either dividing the total frequency into 4 equal parts
or using the answer to part (a) rather than the “0.35” required from the table. “35/100” appeared
fairly frequently and was awarded one mark.

48. This question proved to be a good discriminator. A majority of candidates were able to identify
that the question involved non-replacement and secured the first available mark for sight of
2
“ ”.
7
6
Over a third of candidates went on to give the correct answer or equivalent. However, for
56
others, the inability to manipulate fractions let them down. For example, candidates often used a
3 2 5
correct method but ended their answer with “ × = ” Some candidates accounted for
8 7 56
several different outcomes in their answer.

49. This question was not answered well. Only about a third of the candidates realized that they had
to comment on the frequency of the trials of the experiment. Common unacceptable answers
here were, e.g. “the dice has an equal chance of landing on the numbers” and “if she kept rolling
the dice it would land on a 1”.

50. A considerable number of candidates were able to score full marks on this question.
Most candidates were able to score at least 1 mark in part (a). Common incorrect answers here
include reversing the positions of 1/10 and 9/10 on the bottom right hand branches of the tree
diagram, and giving both pairs of branches on the right hand side of the tree diagram as the
same fractions (usually 7/10 and 3/10).
In part (c), the many candidates were able to write down 1/5 × 7/10 for one of the ways that
Nicola could be late, but neglected to consider the other way (i.e. 4/5 × 1/10). Other common
1 7  4 1 
errors were based on a confusion in the required processes, e.g.  ×  +  ×  ; or in a
 5 10   5 10 
7 1
misunderstanding of how to interpret a tree diagram, e.g. × . Examiners reported a general
10 10
weakness in the candidates’ ability to deal with fractions.
Edexcel GCSE Maths - Probability of Events (H)

51. There were some excellent answers to this question in which a correctly drawn probability tree
was constructed carrying the correct probabilities on each branch. The six required probability
products were then identified leading to the final probability of 67/100. Over 20% of the
candidates got this question fully correct with a further 6% only making one slip. The
alternative methods being used in an attempt to arrive at the final answer did, however, seemed
to be less successful. An abundance of fractions in the subsequent working very often left the
student wondering how to combine them together into one single probability. There was some
evidence of non-replacement seen thus making the question much more difficult than it need
have been.
The fractions manipulation within the working is clearly an area of weakness as some found
difficulty in combining fractions together. For example 5/10 × 7/10 ended up as 35/20, 12/100,
and any other combination of the four numbers. Cancelling the fractions down before
multiplying 5/10 × 7/10 = ½ × 7/10 = 7/20 was fine but then presented a problem when they had
to add together fractions with different denominators. As a general rule it would be easier to
achieve the final result if the fractions are not cancelled down. 60% of the candidates failed to
score any marks on this question. Many had little idea what to do, though realising it involved
the fractions 1/10; 2/10; 7/10 etc, then writing down some simple combination of these
fractions, including multiplying 3 together, adding or taking away. Others had a separate tree
diagram for each spinner, showing one or two throws but were then not sure what to do with
their answers. Candidates using decimal notation also demonstrated correct tree diagrams but
many had difficulty multiplying e.g. 0.2 × 0.2 correctly (the usual answer being 0.4).

52. This was a fairly standard, but non-trivial, probability question. Many successful candidates
drew correct probability tree diagrams and used them properly. 21% of candidates knew that
they had to multiply the probabilities together as they worked along a set of branches starting
with the root and a further 36% of candidates knew they had to be to add the resulting 3
fractions to get the right answer. However, there were a large number of errors due to inability
to tackle the arithmetic of fractions correctly. These were of the following general types:
3 2 5 2 1 3
• carelessness, exemplified by one of × = or × =
9 8 72 9 8 72
4 3 7
• confusion over multiplication, exemplified by all of × = ,
9 8 72
3 2 5 2 1 3
× = and × =
9 8 72 9 8 72
3 2 42 3 2 432
• confusion over multiplication as exemplified by × = or × =
9 8 72 9 8 72
6 2 12 20
• confusion over addition as exemplified by + + =
72 72 72 216
Edexcel GCSE Maths - Probability of Events (H)

Many candidates made life harder for themselves by calculating the correct fractions for the
cases OO, AA and TT, cancelling them and then making an error on the addition of the three
fractions with different denominators.
Some candidates treated the problem as one of replacement and were rewarded as they had
essentially the correct method.
Some candidates thought the total of bottles was 8 or 10 rather than 9 and ended up with a
fraction over 56 or 90 and there were also some candidates who tried to drink 3 bottles or
convert to decimals.
2 2
Other candidates gave fractions such as probability(2nd is O) = rather than .
9 8
Some candidates drew out the whole equally likely sample space for the case with replacement
29
and obtained the answer
81
There were, of course many candidates who tried to draw a probability tree but could not get its
structure correct (generally they did not have 3 branches from every node) and many others who
could not get as far as that.
It was pleasing however to see that fully correct solutions were given in 30% of cases though
44% of candidates scored no marks.
Edexcel GCSE Maths - Probability Tree Diagrams (H)

1. Julie does a statistical experiment. She throws a dice 600 times.

She scores six 200 times.

(a) Is the dice fair? Explain your answer.

.............................................................................................................................

..............................................................................................................................
(1)

Julie then throws a fair red dice once and a fair blue dice once.

(b) Complete the probability tree diagram to show the outcomes.

Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.

Red Blue
Dice Dice

1
Six
6

Not
Six
(3)
(Total 4 marks)

2. Julie does a statistical experiment. She throws a dice 600 times.

She scores six 200 times.

(a) Is the dice fair? Explain your answer.

.....................................................................................................................................

.....................................................................................................................................
(1)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

Julie then throws a fair red dice once and a fair blue dice once.

(b) Complete the probability tree diagram to show the outcomes.

Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.

Red Blue
Dice Dice

1
Six
6

Not
Six
(3)

(c) (i) Julie throws a fair red dice once and a fair blue dice once. Calculate the probability
that Julie gets a six on both the red dice and the blue dice.

....................................

(ii) Calculate the probability that Julie gets at least one six.

.....................................
(5)
(Total 9 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

3. Amy has 10 CDs in a CD holder.

Amy’s favourite group is Edex.
She has 6 Edex CDs in the CD holder.

Amy takes one of these CDs at random.

She writes down whether or not it is an Edex CD.
She puts the CD back in the holder.
Amy again takes one of these CDs at random.

(a) Complete the probability tree diagram.

First choice Second choice EDEX

CD
..........

EDEX
CD NOT-EDEX
0.6 ..........
CD
EDEX
CD
..........
.......... NOT-EDEX
CD

.......... NOT-EDEX
CD
(2)

Amy had 30 CDs.

The mean playing time of these 30 CDs was 42 minutes.

Amy sold 5 of her CDs.

The mean playing time of the 25 CDs left was 42.8 minutes.

(b) Calculate the mean playing time of the 5 CDs that Amy sold.

......................... minutes
(3)
(Total 5 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

4. Amy has 10 CDs in a CD holder.

Amy’s favourite group is Edex.
She has 6 Edex CDs in the CD holder.

Amy takes one of these CDs at random.

She writes down whether or not it is an Edex CD.
She puts the CD back in the holder.
Amy again takes one of these CDs at random.

(a) Complete the probability tree diagram.

First choice Second choice EDEX

CD
..........

EDEX
CD NOT-EDEX
0.6 ..........
CD
EDEX
CD
..........
.......... NOT-EDEX
CD

.......... NOT-EDEX
CD
(2)

(b) Find the probability that Amy will pick two Edex CDs.

.....................
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

Amy had 30 CDs.

The mean playing time of these 30 CDs was 42 minutes.

Amy sold 5 of her CDs.

The mean playing time of the 25 CDs left was 42.8 minutes.

(c) Calculate the mean playing time of the 5 CDs that Amy sold.

......................... minutes
(3)
(Total 7 marks)

5. In a game of chess, you can win, draw or lose.

Gary plays two games of chess against Mijan.

The probability that Gary will win any game against Mijan is 0.55
The probability that Gary will win draw game against Mijan is 0.3

(a) Work out the probability that Gary will win exactly one of the two games against Mijan.

..................................
(3)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

In a game of chess, you score

1 point for a win

1
point for a draw,
2
0 points for a loss.

(b) Work out the probability that after two games, Gary’s total score will be the same as
Mijan’s total score.

..................................
(3)
(Total 6 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

6. Amy is going to play one game of snooker and one game of billiards.

3
The probability that she will win the game of snooker is
4

1
The probability that she will win the game of billiards is
3

Complete the probability tree diagram.

(Total 2 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

7. Amy is going to play one game of snooker and one game of billiards.

3
The probability that she will win the game of snooker is
4

1
The probability that she will win the game of billiards is
3

(a) Complete the probability tree diagram.

(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that Amy will win exactly one game.

…………………….
(3)

Amy played one game of snooker and one game of billiards on a number of Fridays.
She won at both snooker and billiards on 21 Fridays.

(c) Work out an estimate for the number of Fridays on which Amy did not win either game.

…………………….
(3)
(Total 8 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

8. Loren has two bags.

The first bag contains 3 red counters and 2 blue counters.
The second bag contains 2 red counters and 5 blue counters.

Loren takes one counter at random from each bag.

Complete the probability tree diagram.

Counter from Counter from

first bag second bag

Red
2
7

Red
3
5
......
Blue

Red
......
......
Blue

......
Blue

(Total 2 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

9. Loren has two bags.

The first bag contains 3 red counters and 2 blue counters.
The second bag contains 2 red counters and 5 blue counters.

Loren takes one counter at random from each bag.

(a) Complete the probability tree diagram.

Counter from Counter from

first bag second bag

Red
2
7

Red
3
5
......
Blue

Red
......
......
Blue

......
Blue
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that Loren takes one counter of each colour.

...............................................
(3)
(Total 5 marks)

10. Simon plays one game of tennis and one game of snooker.

3
The probability that Simon will win at tennis is
4

1
The probability that Simon will win at snooker is
3
Edexcel GCSE Maths - Probability Tree Diagrams (H)

Complete the probability tree diagram.

tennis snooker

1 Simon
3 wins

Simon
wins
3
4 Simon
.......... does not
win

Simon
.......... wins
Simon
.......... does not
win
Simon
.......... does not
win
(Total 2 marks)

11. Simon plays one game of tennis and one game of snooker.

3
The probability that Simon will win at tennis is
4

1
The probability that Simon will win at snooker is
3
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(a) Complete the probability tree diagram below.

tennis snooker

1 Simon
3 wins

Simon
wins
3
4 Simon
.......... does not
win

Simon
.......... wins
Simon
.......... does not
win
Simon
.......... does not
win

(2)

(b) Work out the probability that Simon wins both games.

.....................................
(2)

(c) Work out the probability that Simon will win only one game.

.....................................
(3)
(Total 7 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

12. Mary has a drawing pin.

When the drawing pin is dropped it can land either ‘point up’ or ‘point down’.
The probability of it landing ‘point up’ is 0.4

Mary drops the drawing pin twice.

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that the drawing pin will land ‘point up’ both times.

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

13. There are two sets of traffic lights on Georgina’s route to school.
The probability that the first set of traffic lights will be red is 0.4
The probability that the second set of traffic lights will be red is 0.3

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that both sets of traffic lights will be red.

.....................................
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(c) Work out the probability that exactly one set of traffic lights will be red.

.....................................
(3)
(Total 7 marks)

14. Julie has 100 music CDs.

58 of the CDs are classical.
22 of the CDs are folk.
The rest of the CDs are jazz.

On Saturday, Julie chooses one CD at random from the 100 CDs.

On Sunday, Julie chooses one CD at random from the 100 CDs.

(a) Complete the probability tree diagram.

(2)

Saturday Sunday
Classical
...........

........... Folk
Classical

........... Jazz
0.58
Classical
...........
0.22 ...........
Folk Folk

........... Jazz
Classical
........... ...........
Jazz ........... Folk

...........
Jazz
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Calculate the probability that Julie will choose a jazz CD on both Saturday and
Sunday.

...................................
(2)

(c) Calculate the probability that Julie will choose at least one jazz CD on Saturday and
Sunday.

...................................
(3)
(Total 7 marks)

15. Tom and Sam each take a driving test.

The probability that Tom will pass the driving test is 0.8

The probability that Sam will pass the driving test is 0.6

(a) Complete the probability tree diagram.

Tom Sam

0.6 Pass

Pass
0.8
............... Fail

0.6 Pass
...............
Fail

............... Fail
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that both Tom and Sam will pass the driving test.

.......................................................
(2)

(c) Work out the probability that only one of them will pass the driving test.

.......................................................
(3)
(Total 7 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

16. Matthew puts 3 red counters and 5 blue counters in a bag.

He takes at random a counter from the bag.
He writes down the colour of the counter.
He puts the counter in the bag again.
He then takes at random a second counter from the bag.

(a) Complete the probability tree diagram.

1st counter 2nd counter

3
8 Red

3 Red
8
........ Blue

........ Red

........
Blue

........ Blue
(2)

(b) Work out the probability that Matthew takes two red counters.

..........................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

17. In a game of chess, a player can either win, draw or lose.

The probability that Vishi wins any game of chess is 0.5

The probability that Vishi draws any game of chess is 0.3

Vishi plays 2 games of chess.

(a) Complete the probability tree diagram.

1st game 2nd game

............... Win

...............
Win Draw

Lose
0.5 ...............

............... Win

0.3 ...............
Draw Draw

Lose
...............

............... ............... Win

...............
Lose Draw

Lose
...............
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that Vishi will win both games.

.....................................
(2)
(Total 4 marks)

18. Julie and Pat are going to the cinema.

The probability that Julie will arrive late is 0.2

The probability that Pat will arrive late is 0.6
The two events are independent.

(a) Complete the diagram.

Pat

late
0.6
Julie

late
0.2
not
late

late

not
late

not
late
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that Julie and Pat will both arrive late.

……………………………
(2)
(Total 4 marks)

19. Salika travels to school by train every day.

The probability that her train will be late on any day is 0.3

(a) Complete the probability tree diagram for Monday and Tuesday.

Monday Tuesday
0.3 late

late
0.3
not
late

late

not
late
not
late
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that her train will be late on at least one of these two days.

……………………………
(3)
(Total 5 marks)

20. Jacob has 2 bags of sweets.

Bag P Bag Q

Bag P contains 3 green sweets and 4 red sweets.

Bag Q contains 1 green sweet and 3 yellow sweets.

Jacob takes one sweet at random from each bag.

(a) Complete the tree diagram.

Bag P Bag Q

green

3 green
7
yellow

green

red

yellow
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Calculate the probability that Jacob will take 2 green sweets.

………………….
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

21. Amy is going to play one game of snooker and one game of billiards.
1
The probability that she will win the game of snooker is
3
3
The probability that she will win the game of billiards is
4
The probability tree diagram shows this information.

Amy played one game of snooker and one game of billiards on a number of Fridays.
She won at both snooker and billiards on 21 Fridays.

Work out an estimate for the number of Fridays on which Amy did not win either game.

…………
(Total 3 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

22. Lucy and Jessica take a test.

The probability that Lucy will pass the test is 0.7

The probability that Jessica will pass the test is 0.4

(a) Complete the probability tree diagram.

Lucy Jessica
pass
0.4

pass
0.7
fail
pass

fail

fail
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that only one of the 2 girls will pass the test.

..............................
(3)
(Total 5 marks)

23. There are 3 boys and 7 girls at a playgroup.

Mrs Gold selects two children at random.

(a) Complete the probability tree diagram below.

1st child 2nd child

boy
............

3 boy
10 ............ girl

boy
............
............ girl

girl
............
(2)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) Work out the probability that Mrs Gold selects two girls.

.....................................
(2)
(Total 4 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

24. Ivan plays a game of darts and a game of snooker.

3
The probability that he will win at darts is
7

6
The probability that he will win at snooker is
11

Complete the probability tree diagram.

Darts Snooker

6
11 Win

3
7 Win

.............. Not Win

.............. Win

Not Win

..............

Not Win
..............
(Total 2 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

25. There are 3 strawberry yoghurts, 2 peach yoghurts and 4 cherry yoghurts in a fridge.

Kate takes a yoghurt at random from the fridge.

She eats the yoghurt.
She then takes a second yoghurt at random from the fridge.

Work out the probability that both the yoghurts were the same flavour.

.....................................
(Total 4 marks)

26. Nicola is going to travel from Swindon to London by train.

1
The probability that the train will be late leaving Swindon is
5

7
If the train is late leaving Swindon, the probability that it will arrive late in London is
10

1
If the train is not late leaving Swindon, the probability that it will arrive late in London is
10
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(a) Complete the probability tree diagram.

leaves Swindon arrives in London

late
............

1 late
5 ............ not late

late
............
............ not late

............ not late

(2)

(b) Work out the probability that Nicola will arrive late in London.

..........................
(3)
(Total 5 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

27. William has two 10-sided spinners.

The spinners are equally likely to land on each of their sides.

BLUE RED BLUE RED

RED BLUE
GREEN BLUE
BLUE RED GREEN BLUE

RED BLUE
BLUE BLUE
GREEN RED BLUE RED

A B

Spinner A has 5 red sides, 3 blue sides and 2 green sides.

Spinner B has 2 red sides, 7 blue sides and 1 green side.

William spins spinner A once.

He then spins spinner B once.

Work out the probability that spinner A and spinner B do not land on the same colour.

..........................
(Total 4 marks)
Edexcel GCSE Maths - Probability Tree Diagrams (H)

28. There are 4 bottles of orange juice,

3 bottles of apple juice,
2 bottles of tomato juice.

Viv takes a bottle at random and drinks the juice.

Then Caroline takes a bottle at random and drinks the juice.

Work out the probability that they both take a bottle of the same type of juice.

....................................
(Total 4 marks)

01. (a) No, as you would expect about 100.

Yes, as it is possible to get 200 sixes with a fair dice 1
B1 for a consistent answer

(b) 3
1 5
, + labels
6 6
5
B1 for on the red dice, not six branch
6
B1 for a fully complete tree diagram with all branches labelled
1 5
B1 for , on all remaining branches as appropriate
6 6
[4]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

02. (a) No, as you would expect about 100.

Yes, as it is possible to get 200 sixes with a fair dice 1
B1 for a consistent answer
(b) 3
1 5
, + labels
6 6
5
B1 for on the red dice, not six branch
6
B1 for a fully complete tree diagram with all branches labelled
1 5
B1 for and on all remaining branches as appropriate
6 6

1
(c) (i) 2
36
2
1
 
6
2
1 1 1
M1   or × only or 0.28
6  6 6
1
A1 or 0.03 or better
36

11
(ii) 3
36
2
5
1−  
6
OR
1 5 5 1 1 1
× + × + ×
6 6 6 6 6 6
2
5 5 5
M2 for 1 −   or 1 – ×
6  6 6
A1 cao
OR
1 5
M1 for × oe
6 6
1 5 5 1
M1 for 2 or 3 only of × , × , “a”
6 6 6 6
11
A1 for or 0.31 or better
36
[9]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

03. (a) 0.4, 0.6

0.4, 0.6,
0.4 2
B1 for LHS: (0.6), 0.4
B1 for RHS: 0.6, 0.4, 0.6, 0.4
(b) 38 3
(30 × 42) – (25 × 42.8) = 1260 – 1070 = 190
190 ÷ 5 =
M1 for (30 × 42) – (25 × 42.8) or 1260 – 1070 or 190 seen
M1 (dep) for “190” ÷ 5
A1 cao
[5]

04. (a) 0.4

0.6,0.4,
0.6,0.4 2
B1 for LHS: (0.6), 0.4
B1 for RHS: 0.6, 0.4, 0.6, 0.4
(b) 0.36 2
0.6 × 0.6
M1 0.6 × “0.6” [0 < “0.6” < 1]
A1 cao
(c) 38 3
(30 × 42) – (25 × 42.8) = 1260 – 1070 = 190
190 ÷ 5 =
M1 for (30 × 42) – (25 × 42.8) or 1260 – 1070 or 190 seen
M1(dep) for “190” ÷ 5
A1 cao 38
[7]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

05. (a) 0.495 3

0.55 × 0.45 × 2
M1 for 0.55 × 0.45 or 0.55 × 0.3 or 0.55 × 0.15 seen
M1 (dep) for 0.55 × 0.45 × 2 or adding 3 or 4
correct terms out of 0.55 × 0.3 × 2 +0.55 × 0.15 ×2
A1 cao
(b) 0.255 3
WL or LW or DD
0.55 × 0.15, 0.15 × 0.55, 0.3 × 0.3
0.165 + 0.09
M1 for 0.55 × 0.15 or 0.3 × 0.3
M1(dep) for adding 2 or 3 correct terms
A1cao
[6]

1
06. on LH branch
4
2 1 2
& & on RH branches 2
3 3 3
B1
B1
[2]

1
07. (a) on LH branch
4
2 1 2
& & on RH branches 2
3 3 3
B1 cao
B1

7
(b) 3
12
3 2 1 1 6 1
× + × = +
4 3 4 3 12 12
3 2 1 1
M1 for × or × from their
4 3 4 3
tree diagram
M1 for sum of two products
7
A1 for oe
12
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(c) 14 3
1 1
n = 21 × 4 or : oe
6 4
1 2
× 84 or 21 ×
6 3
1 3  1 2 1  1
M1 for either ×  =  or ×  =  from their tree
3 4  4 3 4  6
diagram
21
M1 for 21 × 4 (= 84) or ×2
3
A1 for 14 cao
SC: B2 for 63 seen in fraction or ratio
[8]

2 5 2 5
08. , , , 2
5 7 7 7
2
B1 for in the correct place
5
5 2 5
B1 for , , all in the correct place
7 7 7
[2]

2 5 2 5
09. (a) , , , 2
5 7 7 7
2
B1 for in the correct place
5
5 2 5
B1 for , , all in the correct places
7 7 7
Edexcel GCSE Maths - Probability Tree Diagrams (H)

3 5 2 2
(b) × + ×
5 7 5 7
19
3
35
3 5   2 2 
M1 for  ×' '  or ' ' ×' ' 
 5 7   5 7 
3 5   2 2 
M1 (dep) for  ×' '  + ' ' ×' ' 
5 7   5 7 
A1 cao
[5]

1
10.
4
2 1 2
2
3 3 3
1
B1 for correct on tennis
4
2 1 2
B1 for , , correct on snooker
3 3 3
[2]

1
11. (a)
4
2 1 2
2
3 3 3
1
B1 for correct on tennis
4
2 1 2
B1 for , , correct on snooker
3 3 3

3 1
(b) ×
4 3
1
2
4
3 1
M1 for ×
4 3
1
A1 for oe
4
Edexcel GCSE Maths - Probability Tree Diagrams (H)

3 2 1 1
(c) × + ×
4 3 4 3
1 1
+
2 12
7
3
12
3 2  1 1
M1 for ×"  " or "  " ×"  "
4 3 4 3
3 2  1 1
M1 ×"  " + "  " ×"  "
4 3 4 3
7
A1 for oe (0.58…)
12
Or
3 1 1 2
M2 for 1 –  × + × 
4 3 4 3
7
A1 for oe (0.58…)
12
[7]

12. (a) 0.6 2

0.6, 0.4, 0.6
B1 for LHS: (0.4), 0.6
B1 for RHS: (0.4), 0.6, 0.4, 0.6

(b) 0.4 × 0.4 = 0.16 2

4 4
M1 for 0.4 × 0.4 or × oe
10 10
4 16
A1 for 0.16 or or oe
25 100
[4]

13. (a) 0.6 and 0.7, 0.3, 0.7 2

B1 for 0.6 on LH branch
B1 for 0.7, 0.3 and 0.7 on RH branches
(b) 0.4 × 0.3 = 0.12 2
M1 for 0.4 × 0.3
A1 0.12 oe
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(c) 0.4 × 0.7 + 0.6 × 0.3 = 0.46 3

M1 for ‘0.4 × 0.7’ or ‘0.6 × 0.3’
M1 for addition of two products from correct branches
A1 0.46 oe
Alternative
M2 for an attempt to evaluate 1 – (0.3 × 0.4 +’0.6 × 0.7’)
A1 cao
[7]

14. (a) 0.2

0.58, 0.22 0.2 2
B1 0.2 on jazz on 1st set
B1 0.58, 0.22 0.2
repeated 3 times
(b) 0.2 × 0.2 = 0.04 2
M1 ‘0.2’ × ‘0.2’
A1 cao

(c) 0.8 × 0.2 × 2 + 0.2 × 0.2

or
1 – 0.8 × 0.8 = 0.36 3
M1 (0.58+0.22) × ‘0.2’
M1 (0.58 + 0.22) × ‘0.2’ × 2 + ‘0.2’ × ‘0.2’
A1 0. 36 cao
or
M2 1 – (0.58 + 0.22)2
A1 0.36 cao
Listing the outcomes for (c)
CJ 0.58 × ‘0.2’ = 0. 116 FJ 0.22 × ‘0.2’ = 0.044
JC ‘0.2’× 0.58 = 0.116 JF ‘0.2’ × 0.22 = 0.044
JJ ‘0.2’ × ‘0.2’ = 0.04
M2 for all 5 terms added
(M1 for any 2, 3 or 4 terms added)
[7]

15. (a) 0.2 and 0.4, 0.4 2

B1 for 0.2 oe on LH branch
B1 for 0.4 oe on both RH branches
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) 0.8 × 0.6

0.48 2
M1 for 0.8 × 0.6 oe
A1 for 0.48 oe

(c) 0.8 × 0.4 + 0.2 × 0.6

0.44 3
M1 for 0.8 × ‘0.4’ or ‘0.2’ × 0.6 oe
M1 for 0.8 × '0.4’ + '0.2’ × 0.6 oe
A1 for 0.44 oe
OR
M1 for ‘0.2’ × ‘0.4’ oe
M1 for 1 – (‘0.8 × 0.6’ + ‘0.2’ × ‘0.4’) oe
A1 for 0.44 oe
[7]

5
16. (a)
8

5 3 5
, , 2
8 8 8
5
B1 for correct for 1st counter
8
5 3 5
B1 for , , correct for 2nd counter
8 8 8

3 3
(b) ×
8 8
9
oe 2
64
3 3
M1 for ×
8 8
9
A1 for oe
64
[4]

17. (a) Correct diagram 2

B1 for 0.2 oe seen on bottom left branc
B1 for correct probabilities on other branches
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) prob(WW) = 0.5 × 0.5

0.25 2
M1for 0.5 × ‘0.5’
A1ft for 0.25 oe
[4]

18. (a) 0.8,

0.4, 0.6, 0.4 2
B1 for Julie correct
B1 for Pat correct
(b) 0.12 oe 2
0.2 × 0.6
M1 for 0.2 × 0.6
A1 cao
[4]

19. (a) 0.7, 0.7, 0.3, 0.7 2

B1 for Monday correct
B1 for Tuesday correct
(b) 0.51 oe 3
1 − 0.7 × 0.7
M1 for 0.7 × 0.7
M1 for 1 − “0.49”
A1 for 0.51 oe
(M1 for 0. 3 × 0. 3 OR 0.7 × 0.3 OR 0.3 × 0.7
M1 for 0. 3 × 0. 3 + 0.7 × 0. 3 + 0. 3 × 0.7
A1 for 0.51 oe)
[5]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

20. (a) 5 fractions 2

4 1 3 1 3
and , , ,
7 4 4 4 4
B1 for bag P correct
B1 for bag Q correct

3
(b) oe 2
28
3 1
×
7 4
3 1
M1 for ×” “(0 < 2nd fraction < 1)
7 4
A1
[4]

21. 14 3
1 1
n = 21 × 4 or :
4 6
1 2
× 84 or 21 ×
6 3
1 3 1 2 1 1
M1 for ×  =  or ×  = 
3 4 4 3 4 6
21
M1 for 21 × 4 = 84 or ×2
3
A1 cao
[SC:B2 for answer of 63]
[3]

22. (a) 0.6

0.3 0.4
0.6 2
B1 for 0.3
B1 for 0.6, 0.4, 0.6

(b) (0.7 × 0.6) + (0.3 × 0.4)

0.54oe 3
M1 for either 0.7 × “0.6” or “0.3” × “0.4”
M1(dep) for (0.7 × “0.6”) + (“0.3” × “0.4”)
A1 cao
[5]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

23. (a) 7/10 2/9, 7/9 3/9, 6/9 2

B2 for all 5 correct
(B1 for 2, 3, or 4 correct)

42
(b) 2
90
M1 for “1st girl” × “2nd girl”
A1 cao.
[4]

24. 4/7
5/11, 6/11, 5/11 2
B2 for all four probabilities correct
(B1for 1 probability correct)
[2]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

 3 2  2 1  4 3
25.  × + × + × 
9 8 9 8 9 8
6 + 2 + 12
=
72
20
4
72
2 1 3
B1 for or or seen as 2nd probability
8 8 8
3 2 2 1 4 3
M1 for  ×  or  ×  or  × 
9 8 9 8 9 8
3 2 2 1 4 3
M1 for  ×  +  ×  +  × 
9 8 9 8 9 8
20
A1 for o.e.
72
Alternative scheme for replacement
3 2 4
B0 for or or seen as 2nd probability
9 9 9
3 3 2 2 4 4
M1 for  ×  or  ×  or  × 
9 9 9 9 9 9
3 3 2 2 4 4
M1 for  ×  +  ×  +  × 
9 9 9 9 9 9
29
A0 for
81
Special cases
29 20 29
S.C award B2 for or or
81 81 72
2 1 3 3 2 4
SC award B1 for and and or and and seen as
9 9 9 8 8 8
second probability if B2 not scored
Watch for candidates who misread the question and work with
10ths and 9ths They can score M2
Any other total for the number of yoghurts must be identified
before ft
[4]

26. (a) 4/5

(7/10, 3/10) (1/10, 9/10) 2
B2 cao
(B1 for 2 correct from 4/5, (7/10, 3/10), (1/10, 9/10))
Edexcel GCSE Maths - Probability Tree Diagrams (H)

(b) (1/5 × 7/10) + (4/5 × 1/10)

11/50 3
M1 for 1/5 × “7/10” or “4/5” × “1/10” oe selected
M1 for (1/5 × 7/10) + (4/5 × 1/10) oe
A1 for 11/50 oe
[5]

5 7 5 1 3 2 3 1 2 2 2 7
27.  × + × + × + × + × + × 
 10 10   10 10   10 10   10 10   10 10   10 10 
35 + 5 + 6 + 3 + 4 + 14
=
100
OR
 5 2   3 7   2 1 
1 –  ×  +  ×  +  × 
 10 10   10 10   10 10 
10 + 21 + 2 33
=1– = 1−
100 100
67
4
100
M1 for a tree diagram with at most 2 errors
 5 7   5 1 
or one of  ×  or  ×  etc
 10 10   10 10 
M1 for 5 out of 6 correct pairings of different colours
or 2 out of 3 correct pairings of same colours
or 8 out of 9 correct pairings of all colours
M1 (dep on M2) for adding 5 or 6 correct pairings of different
colours
or 1 – (2 or 3 correct pairings of same colours)
67
A1 for oe
100
x
SC All correctly done but 2nd spinner all
9
Award M1 for a “correct tree”
M1 for adding 5 or 6 “correct pairings” of different colours or
1 – (2 or 3 “correct pairings” of same colours)
M0 A0 (answer = 67/90)
[4]
Edexcel GCSE Maths - Probability Tree Diagrams (H)

 4 3   3 2   2 1  12 + 6 + 2
28.  × + × + ×  =
9 8 9 8 9 8 72
20
oe 4
72
3 2 1
B1 for or or seen as 2nd probability
8 8 8
4 3 3 2 2 1
M1 for  ×  or  ×  or  × 
9 8 9 8 9 8
4 3 3 2 2 1
M1 for  ×  +  ×  +  × 
9 8 9 8 9 8
20
A1 for oe
72
Alternative scheme for replacement
4 3 2
B0 for or or seen as 2nd probability
9 9 9
4 4 3 3 2 2
M1 for  ×  or  ×  or  × 
9 9 9 9 9 9
4 4 3 3 2 2
M1 for  ×  +  ×  +  × 
9 9 9 9 9 9
29
A0 for
81
Special cases
29 20 29
S.C. if M0 scored, award B2 for or or
81 81 72
3 2 1
S.C. if M0 scored award B1 for or or
9 9 9
3 2 4
or and and as second probability if B2 not scored
8 8 8
[4]

01. Mathematics A Paper 4

Part (a) was answered well by candidates of all abilities. Acceptable explanations often
5
mentioned 100 as the expected number of sixes. The first mark in part (b) for writing on the
6
“Not Six” branch was gained by many candidates but the tree diagram was often not completed
correctly. Candidates commonly forgot labels, gave incorrect probabilities, or added only one
more branch to the diagram.
Edexcel GCSE Maths - Probability Tree Diagrams (H)

Mathematics B Paper 17
Candidates of all abilities managed to gain credit in part (a) for a reasonable explanation of the
problem. This was well answered. Candidates who failed to score usually offered a
contradictory explanation.
A completely correct tree diagram in part (b) was rare. Most attempts had one branch only from
each of the two given branches. 5/6 was often seen as the probability for the red dice not
showing a six, and this was often the only mark gained.

02. Part (a) required candidates to comment on a statement about a probability. Most thought that
the dice was unfair, maintaining that they would have expected 100 sixes. A few used the
phrase ‘about 100 sixes’. Some did say that the dice was fair, because it is possible to get 200
out of 600 sixes from a fair dice.
Part (b) required candidates to complete a probability tree diagram. Most did so by drawing two
more sets of two branches, correctly labelling and getting full marks. A few candidates thought
that they should just draw 2 out of 4 branches. A few candidates drew the 4 branches but the
probabilities on pairs of branches did not add up to 1.
Part (c) was a standard task and was well done by many candidates. The main error of good
candidates was in (ii) where they interpreted the task as finding exactly one six. However, there
were a sizeable number who thought that
1 × 1 = 2 when multiplying the fractions together.

03. This was truly a question of “two halves”. Part (a) was well answered. Nearly all candidates
correctly gave the 0.4 on the left hand branch, and the majority went on to gain the second
mark, but is was disappointing to find many errors on the right hand side, including careless
reversals of the 0.6 and 0.4, or an apparent desire to make all four probabilities sum to 1. In Part
(b) few gained any marks; there was little understanding of what the calculation of the mean
involves.

04. Mathematics A Paper 6

Parts (a) and (b) were well answered. There were a few candidates who thought the question
was about sampling without replacement.
Part (c) proved to be more of a challenge, with many candidates failing to appreciate that the
key idea involved find the total time for the original 30 CDs and subtracting the total time for
the 5 CDs.
Edexcel GCSE Maths - Probability Tree Diagrams (H)

Mathematics B
Paper 17
All but a minority gained one mark in part (a), usually for a correct probability on the first
branch of the tree diagram.
In part (b) only very few were able to gain any marks, usually 3 or nothing.
Paper 19
Part (a) was well done although some candidates did write the product of two probabilities for
the second choice rather than the probability. The majority of candidates successfully answered
part (b). A common error here was to add rather than multiply the two probabilities. Part (c) was
very poorly done with the majority of candidates having no real idea how to tackle the question.
The common incorrect approach was to calculate the difference between the mean playing times
and subtract this from the mean playing time of all the CDs.

05. This was an unstructured probability question. In the first part candidates had to realise that they
had to use the probability of a ‘not win’ to get 0.55 × 0.45. This then has to be multiplied by 2
and evaluated. Some candidates drew a tree diagram and were able to add together 4 terms to
get the correct answer of 0.495.
In the second part, candidates had to realise that there were three possible cases to consider.
These were ‘win, lose’, ‘lose, win’ and ‘draw, draw’ over the two games. Many candidates were
able to identify at least one of these terms but the overall success rate was not high.
Weaker candidates assumed that all possible cases were equally likely.

06. Specification A
A well answered question. The only common error was to use quarters on the right hand
branches.
Specification B
¼ was often seen in the first pair of branches, gaining one mark, however there were many
confused attempts at completing the second pairs of branches, often still using quarters.

07. Part (a) was generally done well.

In part (b), many candidates knew that they had to multiply and then add the probabilities, but
1 1 2
only about half were able to do this accurately. A common error was × = .
4 3 12
Candidates generally found part (c) of this question difficult. Only the best candidates were able
to achieve all the mark, though there were many that achieved at least one mark- usually for
3 1
writing × . Common answers were 63 and 84- which were awarded two marks.
4 3
Edexcel GCSE Maths - Probability Tree Diagrams (H)

08. This question was usually well answered. Common misunderstandings included a reversal of
the 2/7 and 5/7 on the bottom two branches, or a failure to use 7 in the denominator.

09. Most candidates inserted the correct fractions into the probability tree diagram. Part (b) was also
19
well answered with the correct answer of often seen. Common occurring errors included a
35
correct method, but with the multiplication carried out wrongly by making the denominators of
the fractions the same, followed by incorrect multiplication. A few candidates thought that they
had to add the fractions. They scored no marks.

10. Specification A
The tree diagram was completed correctly by more than half of the candidates. It was not
surprising that most errors were made on the bottom two right hand branches.

Specification B
1
Most candidates scored at least one mark here, usually for correctly labelling the in the first
4
branch. Failure in the second branches often arose from including quarters in one or more of the
probabilities.

11. Specification A
The probability tree diagram was generally completed correctly. Part (b) was almost always
3 1 4
answered using a correct method although there were the occasional errors of × = .
4 3 12
Answers to part (c) were also good, but less successful than part (b). There were the usual errors
of confusing the use of multiplication and addition in the method as well as the accuracy errors
of the type outlined for part (b).

Specification B
The tree diagram in part (a) was completed correctly by over 90% of candidates. Parts (b) and
(c) were generally well answered although more candidates than usual attempted to add rather
than multiply the relevant probabilities. A few candidates indicated that they knew that the
relevant probabilities in (a) needed to be multiplied but then went on to add them regardless.
Edexcel GCSE Maths - Probability Tree Diagrams (H)

12. The majority of candidates were able to complete the tree diagram in part (a). In part (b), most
candidates knew that they were required to multiply 0.4 by 0.4 but a large proportion of these
had problems in doing this- typically giving their answer as 1.6 or 0.8. Relatively few added the
probabilities.

13. Part (a) of this question was done well by the majority of candidates, scoring at least one mark
for 0.6 on the first branch.
In parts (b) and (c), candidates often identified the correct probabilities, but a significant number
were confused about that operations they should be using. A popular error was to add the
probabilities along the branches instead of multiplying them. A surprising number of those
candidates who multiplied probabilities were unable to do this correctly, e.g. 0.3 × 0.4 was often
evaluated as 1.2. In part (c), many candidates worked with the correct two pairs of branches, but
many of these were confused about the order of the operations; a common incorrect method was
(0.6 + 0.7) × (0.6 + 0.3). A popular incorrect answer was 4.6
As the question was written in decimals most candidates kept the probabilities in this form, it
was noted, however, that those candidates who converted their decimals to fractions were often
more accurate with their answers than those that hadn’t.

14. Part (a) was well answered. Very few candidates thought that this was sampling without
replacement.
Answers to part (b) were split between the correct 0.2 × 0.2 and the incorrect 0.2 + 0.2, although
some candidates evaluated the former as 0.4
Answers to part (c) generally considered some of the 5 cases. Quite often the answer 0.2 was
seen from 0.58 × 0.2 + 0.22 × 0.2 + 0.2 × 0.2 or the answer 0.32 from (0.58 × 0.2 + 0.2) × 2
The approach 1 – P(No jazz) was rarely seen, but usually led to the correct answer.

15. Part (a) was done well by the vast majority of the candidates. In part (b), many candidates knew
that they needed to multiply the probabilities but a significant number of these were unable to
do the calculation accurately, e.g. 0.8 × 0.6 = 4.8 or 0.42. Common incorrect methods were 0.8
0.8 + 0.6
+ 0.6 = 1.4 and = 0.7 . In part (c), only the best candidates were able to score full
2
marks for this question, but many were able to score 1 mark for either 0.8 × 0.4 or 0.2 × 0.6.
Common errors here were similar to those in part (b), e.g. those involving poor arithmetic, e.g.
0.8 × 0.4 = 3.2, 0.24 or 2.4, or those involving confusion as to when to multiply the probabilities
or when to add the probabilities, e.g. (0.8 + 0.4) × (0.2 + 0.6).
Edexcel GCSE Maths - Probability Tree Diagrams (H)

16. Accurate completion of the probability tree diagram was good with most candidates scoring at
least one mark. In part (b) however a great many candidates added the probabilities instead of
3 3
multiplying. It is also of note that of the candidates who correctly quoted × a significant
8 8
9
number failed to correctly work out this product; being a common error.
16

17. Very few candidates failed to score any marks at all in this question.
Part (a) was answered very well with most candidates completing the probability tree diagram
correctly. Errors usually occurred on the right hand branches where some candidates put the
values 0.5, 0.3 and 0.2 in the wrong order and some inserted the results of multiplying two
probabilities together. A significant number of candidates were not aware that they needed to
multiply the probabilities on the relevant branches in part (b) and many added 0.5 to 0.5 instead.
Even when candidates did write down 0.5 × 0.5 this was sometimes evaluated incorrectly with
answers of 0.5, 1 and even 2.5 seen quite frequently. Some candidates with incorrect answers
lost the opportunity of gaining a method mark here because they did not show any working.

18. Part (a) was generally well done. However, a number failed to get the correct entries for Pat.
Part (b) could be done independently of the probability tree diagram. Many candidates wrote
down the correct expression of 0.2 × 0.6 and obtained the answer 0.12. However, a significant
number of candidates gave an answer of 1.2. The incorrect method of 0.2 + 0.6 was frequently
seen.

19. Part (a) was well answered. In part (b) the majority of candidates found one product correctly
but few were able to demonstrate a fully correct method often failing to appreciate the
mathematical meaning of ‘at least’. It is disappointing to report that many could not correctly
find the value of the individual products and some final answers were even greater than one.

20. Completion of the tree diagram was well done by the vast majority of candidates. In part (b) a
significant number of candidates added rather than multiplied the probabilities. The main
concern, however, was candidates’ failure to always evaluate the fraction product correctly. It is
worth noting that section B is a calculator section and so the product should not have been a
3 1 4 1
problem. A common error was × = = or, perhaps worse in a probability question,
7 4 28 7
3 1 12 7 84
× = × = =3
7 4 28 28 28
Edexcel GCSE Maths - Probability Tree Diagrams (H)

21. Over 60% of candidates used the probabilities on the tree diagram correctly and indicated that
they would multiply appropriate probabilities. Unfortunately, many arithmetic errors were then
seen; a significant number of candidates added rather than multiplied the probabilities. A
common error was to give the answer as 63 coming from subtracting the number of times both
games were won from the total number of games played.

22. Part (a) was answered correctly by the majority of candidates. Candidates generally had much
less success with part (b) which was poorly done. A significant number of candidates added the
probabilities and then averaged these. Another incorrect method was to find the two correct
products but then multiple these instead of adding them.

23. Candidates clearly understood the concept of a tree diagram and there were many fully correct
answers to this question. A significant minority of candidates however, did not recognise this as
a “non-replacement” situation and marked the same probabilities ( 103 , 107 ) on the second stage of
their diagram. Although these candidates were unable to gain any marks for at least two correct
probabilities in part (a), many used their probabilities correctly in part (b) to gain some credit in
that part of the question. In part (b) some candidates failed to identify the need to multiply two
probabilities and disappointingly, a significant number attempted to add the probabilities,
sometimes giving numbers greater than one as their answers. 13 was often seen following
19
7 + 6 . A number of candidates misread the question and gave the probability of at least one
10 9
girl. Candidates who worked out the correct answer ( 42 ) but failed to simplify their fraction
90
correctly were not penalised as the question was not testing this skill. This does however
confirm the need for candidates to show their method clearly in the space for working. The need
to show working was also highlighted by those candidates who knew they had to multiply, and
wrote this down, but had insufficient ability with fractions to complete this correctly and those
who could not correctly multiply 6 by 7.

24. This question was well understood but it was surprising to see so many candidates making
errors in labelling the probabilities for snooker. The Darts “Not win” was almost correctly
labelled by 96% of candidates but they often switched the probabilities for “win” and “not win”
for snooker.
Edexcel GCSE Maths - Probability Tree Diagrams (H)

25. This was a fairly standard, but non-trivial, probability question. Many successful candidates
drew correct probability tree diagrams and used them properly. 24% of candidates knew that
they had to multiply the probabilities together as they worked along a set of branches starting
with the root and were then able to add the resulting 3 fractions correctly to get the right answer.
However, there were a large number of errors due to inability to tackle the arithmetic of
fractions correctly. These were of the following general types:
3 2 5 2 1 3
• carelessness, exemplified by one of × = or × =
9 8 72 9 8 72
3 2 5
• confusion over multiplication, exemplified by all of × = ,
9 8 72
2 1 3 4 3 7
× = and × =
9 8 72 9 8 72
3 2 42 3 2 432
• confusion over multiplication as exemplified by × = or × =
9 8 72 9 8 72
6 2 12 20
• confusion over addition as exemplified by + + =
72 72 72 216

Many candidates made life harder for themselves by calculating the correct fractions for the
cases SS, PP and CC, cancelling them and then making an error on the addition of the three
fractions with different denominators.
Some candidates treated the problem as one of replacement and were rewarded as they had
essentially the correct method.
Some candidates thought the total of yoghurts was 8 rather than 9 and ended up with a fraction
over 56 and there were also some candidates who tried to eat 3 yoghurts.
2 2
Other candidates gave fractions such as prob. (2nd is S) = rather than .
9 8
Some candidates drew out the whole equally likely sample space for the case with replacement
29
and obtained the answer
81
There were, of course many candidates who tried to draw a probability tree but could not get its
structure correct (generally they did not have 3 branches from every node) and many others who
could not get as far as that. 45% of candidates scored no marks.
Edexcel GCSE Maths - Probability Tree Diagrams (H)

26. A considerable number of candidates were able to score full marks on this question.
Most candidates were able to score at least 1 mark in part (a). Common incorrect answers here
include reversing the positions of 1/10 and 9/10 on the bottom right hand branches of the tree
diagram, and giving both pairs of branches on the right hand side of the tree diagram as the
same fractions (usually 7/10 and 3/10).
In part (c), the many candidates were able to write down 1/5 × 7/10 for one of the ways that
Nicola could be late, but neglected to consider the other way (i.e. 4/5 × 1/10). Other common
1 7  4 1 
errors were based on a confusion in the required processes, e.g.  ×  +  ×  ; or in a
 5 10   5 10 
7 1
misunderstanding of how to interpret a tree diagram, e.g. × . Examiners reported a general
10 10
weakness in the candidates’ ability to deal with fractions.

27. There were some excellent answers to this question in which a correctly drawn probability tree
was constructed carrying the correct probabilities on each branch. The six required probability
products were then identified leading to the final probability of 67/100. Over 20% of the
candidates got this question fully correct with a further 6% only making one slip. The
alternative methods being used in an attempt to arrive at the final answer did, however, seemed
to be less successful. An abundance of fractions in the subsequent working very often left the
student wondering how to combine them together into one single probability. There was some
evidence of non-replacement seen thus making the question much more difficult than it need
have been.
The fractions manipulation within the working is clearly an area of weakness as some found
difficulty in combining fractions together. For example 5/10 × 7/10 ended up as 35/20, 12/100,
and any other combination of the four numbers. Cancelling the fractions down before
multiplying 5/10 × 7/10 = ½ × 7/10 = 7/20 was fine but then presented a problem when they had
to add together fractions with different denominators. As a general rule it would be easier to
achieve the final result if the fractions are not cancelled down. 60% of the candidates failed to
score any marks on this question. Many had little idea what to do, though realising it involved
the fractions 1/10; 2/10; 7/10 etc, then writing down some simple combination of these
fractions, including multiplying 3 together, adding or taking away. Others had a separate tree
diagram for each spinner, showing one or two throws but were then not sure what to do with
their answers. Candidates using decimal notation also demonstrated correct tree diagrams but
many had difficulty multiplying e.g. 0.2 × 0.2 correctly (the usual answer being 0.4).
Edexcel GCSE Maths - Probability Tree Diagrams (H)

28. This was a fairly standard, but non-trivial, probability question. Many successful candidates
drew correct probability tree diagrams and used them properly. 21% of candidates knew that
they had to multiply the probabilities together as they worked along a set of branches starting
with the root and a further 36% of candidates knew they had to be to add the resulting 3
fractions to get the right answer. However, there were a large number of errors due to inability
to tackle the arithmetic of fractions correctly. These were of the following general types:
3 2 5 2 1 3
• carelessness, exemplified by one of × = or × =
9 8 72 9 8 72
4 3 7
• confusion over multiplication, exemplified by all of × = ,
9 8 72
3 2 5 2 1 3
× = and × =
9 8 72 9 8 72
3 2 42 3 2 432
• confusion over multiplication as exemplified by × = or × =
9 8 72 9 8 72
6 2 12 20
• confusion over addition as exemplified by + + =
72 72 72 216

Many candidates made life harder for themselves by calculating the correct fractions for the
cases OO, AA and TT, cancelling them and then making an error on the addition of the three
fractions with different denominators.
Some candidates treated the problem as one of replacement and were rewarded as they had
essentially the correct method.
Some candidates thought the total of bottles was 8 or 10 rather than 9 and ended up with a
fraction over 56 or 90 and there were also some candidates who tried to drink 3 bottles or
convert to decimals.
2 2
Other candidates gave fractions such as probability(2nd is O) = rather than .
9 8
Some candidates drew out the whole equally likely sample space for the case with replacement
29
and obtained the answer
81
There were, of course many candidates who tried to draw a probability tree but could not get its
structure correct (generally they did not have 3 branches from every node) and many others who
could not get as far as that.
It was pleasing however to see that fully correct solutions were given in 30% of cases though
44% of candidates scored no marks.
Edexcel GCSE Maths - Sample Space Diagrams (FH)

1. Joe rolls a 6-sided dice and spins a 4-sided spinner.

The dice is labelled 1, 2, 3, 4, 5, 6

The spinner is labelled 1, 2, 3, 4

3
4
2

1
Joe adds the score on the dice and the score on the spinner to get the total score.

He records the possible total scores in a table.

+ 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3
3 4
4 5

(a) Complete the table of possible total scores.

(2)

(b) Write down all the ways in which Joe can get a total score of 5
One of them has been done for you.

(1, 4), .....................................

(2)

(c) Write down all the ways Joe can get a total score of 8 or more.

…………………......................................
(2)
(Total 6 marks)
Edexcel GCSE Maths - Sample Space Diagrams (FH)

2. The diagram shows a 3-sided spinner and an ordinary dice.

red
gre 1

blue
en

The spinner has 1 green side, 1 blue side and 1 red side.

Alex spins the spinner once and rolls the dice once.

Write down all the possible outcomes.

One has already been done for you.

(g, 1) ......................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................
(Total 2 marks)

01. (a) 45678 2

56789
6 7 8 9 10
B2 if fully correct
(B1 for 1 row correct or 2 columns correct)

(b) (1, 4); (2, 3); (3, 2); (4, 1) 2

B2 if fully correct
(B1 for either (2, 3) or (3, 2))

(c) (2, 6); (3, 5); (3, 6); (4, 4); (4, 5); (4, 6) 2
B2 if fully correct (order in brackets need not be consistent)
(B1 for 3 pairs correct, ignore extras)
[6]
Edexcel GCSE Maths - Sample Space Diagrams (FH)

02. (g,1) (g,2) (g,3) (g,4) (g,5) (g,6) (b,1) (b,2)(b,3) (b,4) (b,5) (b,6)
(r,1) (r,2) (r,3) (r,4) (r,5) (r,6) 2
B2 for a fully correct list
[B1 for at least 6 correct additional outcomes]
Ignore duplicates e.g. (g,1) (1, g)
[2]

01. Foundation Tier

This question was well understood and candidates usually obtained full marks in part (a) though
in parts (b) and (c) candidates usually only wrote down partial solutions.
Intermediate Tier
Part (a) was answered very well indeed. Almost three quarters of the candidates were successful
in part (b). Some candidates only gave either (2, 3) or (3, 2) for the answer, not appreciating that
(dice 2, spinner 3) is different from (dice 3, spinner 2). Almost all candidates were able to list at
least three correct pairs in part (c). Some repeated pairs in reverse order, e.g. (2, 6) and (6, 2),
despite 4 being the highest number on the spinner, and some failed to list all the pairs. Some
candidates ignored “or more” and only listed the three pairs that give a score of 8. It was
common to see pairs such as (1, 7) that included impossible values.

02. This question proved to be very successful with 55% of candidates being able to write out the
missing 17 combinations successfully. One mark was obtained by 25% of candidates that could
give an additional 6 outcomes but 20% scored no marks. Interestingly a significant number of
candidates thought there were only 3 numbers on the dice since only 1, 2 and 3 were shown in
the diagram. The most successful candidates gave their combinations in an ordered fashion,
either by all the greens followed by all the blues followed by all the reds or by all the ones, all
the twos etc.
Edexcel GCSE Maths - Two Way Tables (FH) 1

1. 70 students each chose one P.E. activity.

They chose one of basketball or swimming or football.
The two-way table shows some information about their choices.

Basketball Swimming Football Total

Female 10 37
Male 17
Total 19 22 70

(a) Complete the two-way table.

(3)

One of these students is picked at random.

(b) Write down the probability that this student chose basketball.

.........................................
(2)
(Total 5 marks)

2. The two-way table shows some information about the colours of Ford cars and of Toyota cars in
a garage.

white blue red Total

Ford 5 21
Toyota 7
Total 9 16 40

(a) Write down the total number of white cars.

.....................................
(1)
Edexcel GCSE Maths - Two Way Tables (FH) 1

(b) Complete the two-way table.

(3)

(c) One of these 40 cars is to be picked at random.

Work out the probability that this car will be blue.

.....................................
(1)
(Total 5 marks)

01. (a) 10 12 15 37 3
9 17 7 33
19 29 22 70
B3 all correct
(B2 for 4 or 5 entries correct)
(B1 for 2 or 3 entries correct)

19
(b) 2
70
19
B2 for , accept 0.27 (....)
70
k
(B1 for with 0 < k < 10 or for the correct probability
70
incorrectly expressed, eg ‘19 out of 70’)
[5]

02. (a) 9 1
B1 cao
(b) 5 9 7 21 3
4 7 8 19
9 16 15 40
B3 for all correct
(B2 for 4 or 5 correct)
(B1 for 1 or 2 or 3 correct)
Edexcel GCSE Maths - Two Way Tables (FH) 1

16
(c)
40
2
= 1
5
B1 for 2/5 oe
[5]

01. This question was answered well. In part (a), more than 80% of candidates completed the two-
way table correctly and almost three quarters of candidates gave the correct probability in part
(b).

02. Foundation Tier

This question was well understood and candidates were usually able to score some marks on
this question, although the inability in some cases to fill in any of the numbers correctly in the
two-way table was surprising. Incorrect notation for probability such as 16 out of 40 and 16:40
were often seen. Other errors on this part of the question were words such as likely or unlikely.
Intermediate Tier
Part (a) was answered extremely well. Some candidates gave the number of white Toyota cars
rather than the total number of white cars. Only a handful of candidates failed to score any
marks in part (b) with most completing the two-way table correctly. More than 80% of
candidates gave the correct probability in part (c). Very few wrote a probability using incorrect
notation.
Edexcel GCSE Maths - Two Way Tables (FH) 2

1. The table shows some information about five children.

Name Gender Age Hair Colour

Aaron Male 6 Black
Becky Female 10 Brown
Kim Female 6 Brown
Darren Male 9 Blonde
Emily Female 4 Red

(a) Write down the colour of Darren’s hair.

.....................................
(1)

(b) Write down the name of the oldest child.

.....................................
(1)

(c) Work out the mean of the ages of the children.

.....................................
(2)
(Total 4 marks)

2. The two-way table gives some information about how 100 children travelled to school one day.

Walk Car Other Total

Boy 15 14 54
Girl 8 16
Total 37 100
Edexcel GCSE Maths - Two Way Tables (FH) 2

(a) Complete the two-way table.

(3)

One of the children is picked at random.

(b) Write down the probability that this child walked to school that day.

.....................................
(1)

One of the girls is picked at random.

(c) Work out the probability that this girl did not walk to school that day.

.....................................
(2)
(Total 6 marks)

3. The two-way table gives some information about how 100 children travelled to school one day.

Walk Car Other Total

Boy 15 14 54
Girl 8 16
Total 37 100

(a) Complete the two-way table.

(3)
Edexcel GCSE Maths - Two Way Tables (FH) 2

One of the children is picked at random.

(b) Write down the probability that this child walked to school that day.

.....................................
(1)
(Total 4 marks)

4.

The diagram shows some 3-sided, 4-sided and 5-sided shapes.

The shapes are black or white.

(a) Complete the two-way table.

Black White Total

3-sided shape 4 5

4-sided shape 2

5-sided shape 0

Total 11
(3)
Edexcel GCSE Maths - Two Way Tables (FH) 2

Ed takes a shape at random.

(b) Write down the probability the shape is white and 3-sided.

.....................
(2)
(Total 5 marks)

5. The two-way table shows some information about the number of students in a school.

Year Group Total

9 10 11
Boys 125 407
Girls 123
Total 303 256 831

Complete the two-way table.

(Total 3 marks)
Edexcel GCSE Maths - Two Way Tables (FH) 2

6. A factory makes three sizes of bookcase.

The sizes are small, medium and large.

Each bookcase can be made from pine or oak or yew.

The two-way table shows some information about the number of bookcases the factory makes
in one week.

Small Medium Large Total

Pine 7 23
Oak 16 34
Yew 3 8 2 13
Total 20 14

Complete the two-way table.

(Total 3 marks)

7. 80 children went on a school trip.

They went to London or to York.

23 boys and 19 girls went to London.

14 boys went to York.

(a) Use this information to complete the two-way table.

London York Total

Boys
Girls
Total
(3)
Edexcel GCSE Maths - Two Way Tables (FH) 2

One of these 80 children is chosen at random.

(b) What is the probability that this child went to London?

........................................
(1)
(Total 4 marks)

01. (a) Blonde 1

B1 for blond or blonde
Accept different spelling as long as intention is clear.

(b) Becky 1
B1 cao
Accept different spelling as long as intention is clear.

(c) (6 + 10 + 6 + 9 + 4) ÷ 5
7 2
M1 for attempt to add the 5 ages (condone 1 error) and divide
by 5
A1 cao
[4]

02. (a)
15 25 14 54
22 8 16 46
37 33 30 100

Table 3
B3 for all 5 correct
(B2 for 3 or 4 correct)
(B1 for 1 or 2 correct)

37
(b) 1
100
37
B1 oe
100
Edexcel GCSE Maths - Two Way Tables (FH) 2

24
(c) 2
46
" '46' −'22' "
B2 for oe, ft from no of girls
'46'
(B1 16 + 8 or 24 or ‘46’ seen)
[6]

03. (a)
15 25 14 54
22 8 16 46
37 33 30 100

Table 3
B3 for all 5 correct
(B2 for 3 or 4 correct)
(B1 for 1 or 2 correct)

37
(b) 1
100
37
B1 oe
100
[4]

04. (a) 1 (4) (5),

(2) 2 4,
2 (0) 2,
5 6 (11) 3
B3 for all 7 missing values correct
(B2 for 5 or 6 missing values correct)
(B1 for 3 or 4 missing values correct or 2 bottom row numbers
total to 11)

4
(b) 2
11
(B2 accept as recurring decimal 0.3636…)
 n 4
(B1 for denominator of 11,   or numerator of 4,   or
 11  n
decimal written as 0.36)
[5]
Edexcel GCSE Maths - Two Way Tables (FH) 2

05. 149, 133 125, 407

154, 123, 147, 424
303, 256, 272, 831 3
B3 for fully correct table.
(B1 for 2 or 3 correct entries)
(B2 for 4 or 5 correct entries)
[3]

06. 7 12 4 23
10 16 8 34
3 8 2 13
20 36 14 70 3
B3 for fully correct table
(B2 for 4 or 5 correct entries,
B1 for 2 or 3 correct entries)
[3]

07. (a) 23 14 37
19 24 43
42 38 80 3
B3 for all correct
(B2 for 5, 6, 7 or 8 correct)
(B1 for any 2 of the 4 given correctly placed)

42
(b) 1
80
"42"
B1 for oe
"80"
[4]

01. The first two parts of this question were well answered with about 99% of candidates giving
correct answers. Part (c) proved to be much more of a challenge with a large proportion of
candidates giving “6” as their answer. This seemed to indicate confusion between the mean and
median or the mean and mode. A small but significant number of candidates gave the sum of
the ages (35) as their answer. Some candidates gave “31.8” as their answer here without
working, which seemed to indicate a misuse of their calculator.
Edexcel GCSE Maths - Two Way Tables (FH) 2

02. Foundation
The two-way table in part (a) was usually completed accurately, although a number of
arithmetic errors were in evidence. In the table, the car column caused the most problems for
candidates.
37
In part (b), the correct answer of (or 0.37 or 37%) was the most common response.
100
Answers of 37 and 1/37 were also seen. There were also several who did not realise a numerical
answer was required, responding with “unlikely”
In part (c), most candidates scored at least one mark for using either 46 or 24 in their working.
Many failed to score full marks with answers of 1/46 and 24/100 being common errors. Some
failed to see “not”, giving an answer of 22/46. Following the correct answer in (b), many
63
candidates gave as their answer in (c), having not fully read the question correctly.
100
There were less candidates giving unacceptable notation but ratio and ‘out of’ were still seen on
several occasions.

Higher
Points were usually plotted correctly although a few candidates clearly missed this part of the
question. A number initially misread the table horizontally and so plotted (65, 80) but then
realised and rectified their mistake when unable to plot (100, 110) on the axes provided. In part
(b) the majority of candidates chose to describe a dynamic relationship along the lines of “the
taller the sheep, the longer it is” rather than just stating positive correlation. Incorrect answers
most commonly seen involved “direct proportion” or an expression of the difference between
the variables. A number referred to weight of sheep rather than height. In part (c) neither a line
of best fit nor vertical line at 76cm was usually seen. Instead candidates judged the value by eye
and in most cases gained full marks by being within the acceptable range of answers. Errors that
did occur were due to the 2 axes being confused or misreading of the vertical scale.

03. This question was answered well by the vast majority of candidates.
The most common errors in part (a) were due to the failure to carry out simple additions and
subtractions accurately with incorrect entries seen most often in the ‘Car’ column. Some
candidates failed to notice the empty space in the ‘Total’ column and left this blank. In these
cases it was apparent that candidates had not carried out a horizontal check as well as a vertical
one. The probability in part (b) was usually correct.

04. Again this was a well-understood question with 91% of candidates able to complete the two-
way table using the information given in the question. There was less success in part (b) though
53% of candidates scored both marks and 23% gained partial credit for writing 4 over a
denominator or a numerator over 11. When candidates wrote the probability as “4 out of 11”
they scored no marks. Fortunately these occurrences are becoming less common though it was
alarming to see many candidates writing the probability as “4”!
Edexcel GCSE Maths - Two Way Tables (FH) 2

05. About two thirds of candidates scored full marks by giving a fully correct and complete two-
way table. 7% of candidates scored 2 marks (for 4 or 5 correct entries) with a further 12%
scoring 1 mark (for 2 or 3 correct entries).

06. About two thirds of the candidates were able to score full marks for completing the two-way
table accurately. Calculation slips were the most frequent cause for errors, but a significant
number of candidates lost a mark for writing 140 in the bottom right hand corner of the table.

07. Questions on two-way tables are often to be found on these papers and this paper was no
exception. However, the success rate was not as high as on previous papers because this time
the candidates had to fill in ALL the numbers on the table rather than just fill in the gaps.
This resulted in many not having a correct table because they either did not read the wording
correctly or misunderstood what was given.
Many students did not read the first line of information and so many did not put the number 80
on the table. Others saw that 14 boys went to York and then assumed that this meant that no
girls went to York.
By far the most common error was to have the second row of the table as 19, 0, 19 which
generally meant that they had a total of 56 children on the school trip.
In part (b) there were quite a few correct answers or correct from their table but there were still
those students who scored no marks because they gave their probability as a ratio which is not
acceptable.
Over 31% scored all 4 marks with a further 36% scoring 3 marks and another 25% scoring 2
marks.