Sets 3
3 marks · EasyIn a survey of 60 people:
• 36 people like apples (A),
• 24 people like bananas (B),
• 12 people like both apples and bananas.
A person is chosen at random from the survey.
Work out the probability that the person likes both apples and bananas.
Work out the probability that the person likes bananas given that they like apples.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 0.2 · must show Correctly computes 12/60
(b) 1/3 · must show Correctly computes 12/36 or gives 0.33 or 1/3
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Works out P(A ∩ B) = 12/60 = 0.2 or 1/5
M1 (b) · 1 mark · Recognises conditional probability needs n(A ∩ B)/n(A), sets up fraction 12/36.
A2 (b) · 1 mark · Evaluates 12/36 = 1/3 or 0.33
Worked solution
a) Probability likes both = n(A ∩ B)/n(U) = 12/60 = 0.2
b) Probability likes bananas given they like apples = n(A ∩ B)/n(A) = 12/36 = 1/3 ≈ 0.33