UNIT 12 Question 3
41 marks from 41 questions
Question 1
The probability of an event not happening is always 1 minus the probability that it will happen.
a. True
b. False
The probability of getting an even number on this fair spinner is:
Question 2
a.
b.
c.
Question 4
The probability of getting an odd number on this fair spinner is:
A fair spinner has sections of four colours: green, red, blue and yellow.
a. The spinner landing on red and the spinner landing on green are mutually exclusive outcomes because:
a. the spinner cannot land on both red and green
b.
b. red and green are not the only colours on the spinner
c. c. red and green are equally likely
Question 5
The probabilities of all mutually exclusive outcomes add up to .
Question 6
If the probability of winning a football match is 0.55 and the probability of losing is 0.2, what is the
probability of drawing?
a. 0.25
b. 0.35
c. 0.75
Question 7 Question 11
The probability of getting tails when you flip a coin is 50%. This means that if you flip 10 coins, you will Kristyna’s brother packs her school lunch each day.
always get 5 tails.
The probability that she will have a banana in her lunch is .
a. True
b. False The probability of having an apple is and an orange is .
What is the probability that on one particular day Kristyna will have either an apple or an orange?
Question 8 Give your answer as a fraction in its lowest terms.
The probability that I get tails when I flip a biased coin is . The probability of getting heads is
a.
b.
Question 12
c.
The table shows the number of students who play sport at a school.
Football Swimming Tennis
Question 9
A fair spinner has ten equal sections. Two are red, three are blue and the rest are green. The spinner is Girls 15 18 12
spun once. What is the probability of it landing on red or green?
a. Boys 21 10 9
b.
A girl is chosen at random. What is the probability that she swims?
c.
Give your answer as a decimal.
Question 10
Li writes the letters of the word MATHEMATICS on separate cards and puts them in a bag. She picks a Question 13
card at random. What is the probability that she doesn’t pick a vowel?
The probability of selecting at random a red counter from a bag that contains red and yellow counters
only is . There are 27 yellow counters in the bag. What is the total number of counters in the bag?
Question 14 Question 17
A multipack of crisps contains plain, salt and vinegar, cheese and onion and prawn cocktail flavours.
The probabilities of randomly selecting each flavour are given in the table.
Flavour Plain Salt and vinegar Cheese and onion Prawn cocktail
Probability
There are nine packets of cheese and onion crisps in the multipack. P(HH) =
How many packets of salt and vinegar crisps are there?
Question 18
Question 15
Danilo is rolling a fair 8-sided dice with sides numbered 1, 2, 3, 4, 5, 6, 7, and 8. He rolls it 200 times.
How many times is he likely to get a number that is a factor of 10?
A and B are complementary events.
What is the missing probability on the lower branch?
Question 16
P(CC) =
Question 19 Question 21
Adira took two marbles from a bag containing three yellow marbles and two blue marbles, replacing Mikel has five red, seven brown and eight blue T-shirts.
the first marble before selecting the second one.
He also has two blue, three brown and five black jackets.
What is the probability that Mikel will be wearing the same colour T-shirt and jacket?
Question 22
2% of the world’s population have naturally blonde hair, 1.5% have red and 74% have dark brown
hair.
10% of the population are left-handed.
55% of the population have brown eyes while only 2% have green eyes.
Claudette says that it is more likely to meet a left-handed person with green eyes and brown hair than
What is the probability that the marbles were both yellow?
a right-handed person with brown eyes and red hair.
P(YY) = × = Is she correct?
a. Yes
b. No
Question 20
Question 23
This tree diagram shows outcomes when rolling a dice and tossing a coin. There are three sets of traffic lights along a road. If each light is green for of the time, what is the
probability that a driver on this road is stopped by exactly one of these lights?
What is the probability of getting a five or six on the dice AND a tail on the coin?
(Enter your answer as a simplified fraction.) A tree diagram will help in your calculations.
P(5 or 6, T) =
Question 24 Question 27
Which equation is correct? The results from a dice-rolling experiment are shown in the table.
Outcome Frequency
a. Relative frequency = b. Relative frequency =
One 6
Two 8
Three 5
Question 25
Four 6
Loren entered the triple jump and the hurdles.
Five 3
She has a 65% chance of winning the triple jump and an 80% chance of winning the hurdles. Six 7
What is the probability she wins at least one of these events? The relative frequency of rolling a four is:
Hint: Draw a probability tree with this structure to help your calculations. 6
Question 28
Outcome Tally
Heads
Tails
P(at least one win) = %
Above are the results of a coin-flipping experiment.
Question 26 The relative frequency of tails is %.
Question 29
Number of matches29303132
Number of boxes 186214 6
Ten dice were rolled and a five occurred three times.
A box of matches is supposed to contain 30 matches. However, this number varies slightly between
What was the relative frequency of five? boxes.
The table shows a survey of 100 boxes.
If one of these boxes were selected at random, what is the probability that it would contain exactly 30
matches?
Give your answer as a percentage.
%
Question 30 Question 33
Outcome Tally Holly surveyed learners about their favourite subject:
Two heads Five learners preferred science, eight preferred maths and seven preferred English
One head and one tail
From this data, what is the experimental probability that the next student she questions will select
Two tails maths?
The relative frequency of the most frequent outcome is %. Give your answer as a percentage.
Question 31
A coin was tossed several times. Question 34
The relative frequency of tossing a head was 0.59.
A bag contains eight tiles. Each tile has a letter on it.
The letters are A, C, D, E, G, K, L and N.
What was the relative frequency of tossing a tail?
A tile is taken from the bag.
Two events are:
V: the letter is either A or E
Question 32
W: the letter is in the word LAND.
Hans drew a counter out of a bag, recorded its colour and then replaced it. Event V has happened.
He did this 20 times and recorded the results. What is P(W) now?
Red 7
P(W) =
Blue 11 2
Yellow 2
From this data, what is the probability that the next counter will be red? Question 35
Give your answer as a fraction in its simplest form.
Two events M and N are independent.
Which of these statements are true?
Select all correct statements.
a. The probability of N happening will not affect the probability of M happening.
b. The probability of N happening changes the probability of M happening.
c. The probability of M happening will not affect the probability of N happening.
Question 36 Question 39
P and Q are two events. Two fair dice are rolled. Two events are:
The probability of P happening is different if Q happens than if Q does not happen. A: the score on the first dice is a 6
P and Q ___________ events. B: the score on the second dice is a 6
Select the correct words to complete this sentence. Which of these statements is true?
a. are not independent a. The events are not independent because the events give the same score.
b. are independent b. The events are independent because the score on one dice does not affect the score on the other.
Question 37 Question 40
A dice is rolled 60 times and the number of times a six is rolled is recorded. This is repeated four times. The letters of the word INSTRUMENTAL are each written onto a card and placed in a bag. One letter is
taken out at random.
Total number of rolls 60 120 180 240 There are two events.
A: the letter is a vowel
Total number of times a 6 is rolled 10 18 25 30
B: the letter is in the word NEAT
What happens the relative frequency of rolling a six on the dice? What is the probability of event B if event A happens?
a. It decreases Give the answer as a fraction in its simplest form.
b. It stays the same
P(B) =
c. It increases
Question 38
A coin is flipped twice.
Two events are:
F: the first flip is a tail
B: both flips are tails
F does not happen.
What is the probability that B happens?
Question 41
A bag contains seven red and six green balls.
A ball is chosen at random and then replaced.
Then a second ball is chosen at random.
Two events are:
F: the colour of the first ball is red
S: the colour of the second ball is green
If event F does not happen, what is the probability of event S happening?
P(S) =
