Question 1
LEVEL 4
Shivani flips a coin twice. What is the probability that at least one of the outcomes is heads.
Select the correct answer from the list below:
A: 0.5
B: 0.25
C: 0.75
D: 0.\dot{6}
CORRECT ANSWER: C: 0.75
WORKED SOLUTION:
To simplify this problem we can represent the probabilities using a tree diagram.
There is only one branch where heads is not one of the outcomes. We can therefore subtract the probability of this branch from 1 to find the correct likelihood.
P(\text{at least one heads}) = 1 - P(T,T) = 1 - 0.25 = 0.75
Alternatively we can add up the probabilities of the other three branches
P(\text{at least one heads}) = P(H,H) + P(H,T) + P(T,H) = 0.25 +0.25 +0.25 = 0.75
Question 2
LEVEL 4
There are 10 coloured cubes in a bag.
6 of them are purple and the rest are green.
Jared picks one then replaces it.
He then picks another.
What is the probability that both cubes selected are purple?
Select the correct answer from the list below:
A: 0.36
B: 0.24
C: 0.16
D: 0.64
CORRECT ANSWER: A: 0.36
WORKED SOLUTION:
To simplify this problem we can represent the probabilities using a tree diagram.
There is only one branch where purple appears twice. Therefore the probability that both cubes are purple is 0.36
Question 3
LEVEL 4
Billie takes part in two races during her sports day, the egg and spoon race and the sack race.
The probabilities of her winning and losing at the individual events can be seen in the tree diagram below.
What is the probability of her winning exactly one event?
Select the correct answer from the list below:
A: 0.42
B: 0.21
C: 0.58
D: 0.09
CORRECT ANSWER: A: 0.42
WORKED SOLUTION:
We can calculate the probabilities for the outcomes of both events.
There are two branches where Billie wins exactly one event, where she wins then loses and loses then wins.
Therefore to calculate the probability of her winning exactly one event, we need to add these two probabilities up.
P(Winning exactly one event) = 0.21 + 0.21 = 0.42
Question 4
LEVEL 4
The probability of Bryony passing her Geography exam is 0.75
The probability of her passing her Science exam is 0.65
What is the probability that she passes at least one exam?
Select the correct answer from the list below:
A: 0.9125
B: 0.0875
C: 0.4875
D: 0.5125
CORRECT ANSWER: A: 0.9125
WORKED SOLUTION:
To simplify this problem we can represent the probabilities using a tree diagram.
There are three branches where she passes at least one exam.
Therefore to calculate the probability of her passing at least one exam, we can add those probabilities together or subtract the probability of her failing both exams from 1.
P(Passing at least one exam) = 1 - 0.0875 = 0.9125
Question 5
LEVEL 4
Ewan visits the fun fair. He plays Huck a duck and Rifle shooting.
The probability that he wins a prize on Huck a Duck is 0.7 and the probability that he wins on rifle shooting is 0.1
What is the probability that he wins at least at least one prize?
Select the correct answer from the list below:
A: 0.73
B: 0.63
C: 0.66
D: 0.93
CORRECT ANSWER: A: 0.73
WORKED SOLUTION:
To simplify this problem we can represent the probabilities using a tree diagram.
There are three branches where he wins at least one prize.
Therefore to calculate the probability of him winning at least one prize, we can add those probabilities together or subtract the probability of him winning no prize from 1.
P(Winning at least one prize) = 1 - 0.27 = 0.73