16 The probability that it will rain on Saturday is 0.
8
If it rains on Saturday, the probability that it will rain on Sunday is 0.65
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If it does not rain on Saturday, the probability that it will rain on Sunday is 0.4
(a) Use this information to complete the probability tree diagram.
Saturday Sunday
rain
....................
rain
0.8
....................
does not rain
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rain
....................
....................
does not rain
....................
does not rain
(2)
(b) Work out the probability that it will rain on just one of these two days.
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.......................................................
(3)
(Total for Question 16 is 5 marks)
15
*P48490A01524* Turn over
14 There are 52 cards in a pack.
12 cards are picture cards.
40 cards are number cards.
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Melina takes at random a card from the pack.
She keeps the card and then takes at random a second card from the remainder of the pack.
(a) Complete the probability tree diagram.
First card Second card
picture
...........................
card
picture
card
...........................
number
...........................
card
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picture
...........................
card
...........................
number
card
number
...........................
card
(3)
(b) Work out the probability that the two cards Melina takes are both picture cards or
both number cards.
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.......................................................
(3)
(Total for Question 14 is 6 marks)
14
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8 A box contains toy cars.
Each car is red or blue or black or silver.
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Emily takes at random a car from the box.
The table shows the probabilities that Emily takes a red car or a blue car or a black car.
Colour of car Probability
red 0.20
blue 0.05
black 0.15
silver
(a) Work out the probability that Emily takes a silver car.
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......................................................
(2)
Emily puts the car back into the box.
There are 6 blue cars in the box.
(b) Work out the total number of cars in the box.
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......................................................
(2)
(Total for Question 8 is 4 marks)
7
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16 In a bag there is a total of 20 coins.
10 coins are 20 cent coins
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6 coins are 10 cent coins
4 coins are 5 cent coins
Emma takes at random two of the coins from the bag.
(a) Complete the probability tree diagram.
(2)
First coin Second coin
.............. 20 cent coin
..............
20 cent coin 10 cent coin
..............
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10 5 cent coin
20
..............
20 cent coin
.............. ..............
10 cent coin 10 cent coin
..............
5 cent coin
..............
.............. 20 cent coin
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..............
5 cent coin 10 cent coin
..............
5 cent coin
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(b) Work out the probability that Emma takes two 5 cent coins.
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........................................................
(2)
(c) Work out the probability that the total value of the two coins is 20 cents or less.
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........................................................
(3)
(Total for Question 16 is 7 marks)
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17
*P45863A01724* Turn over
21 Each student in a group of 32 students was asked the following question.
“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”
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Their answers showed that
19 students have a desktop computer
17 students have a laptop
16 students have a tablet
9 students have both a desktop computer and a laptop
11 students have both a desktop computer and a tablet
7 students have both a laptop and a tablet
5 students have all three.
(a) Using this information, complete the Venn diagram to show the number of students in
each appropriate subset.
D L
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............................ ............................ ............................
............................
.................. . . . . . . . . . . ............................
............................
T
............................
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(3)
One of the students with both a desktop computer and a laptop is chosen at random.
(b) Find the probability that this student also has a tablet.
........................................................
(1)
(Total for Question 21 is 4 marks)
22
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