CIE iGCSE Maths E8.4 Conditional probability Exam Style Practice Questions- Paper 2
75 people are asked if they have a car, C, and if they have a job, J.
The Venn diagram shows the results.
A person is chosen at random from those who have a car.
Find the probability that this person also has a job.
▶️ Answer/Explanation
Ans: 17/20
From the Venn diagram:
People with cars (C) = 9 (C∩J) + 51 (C only) = 60
People with jobs among car owners = 9 (C∩J)
The Venn diagram shows:
• People with both car and job (C∩J) = 51
• People with car only = 9
• Therefore probability = 51/(51+9) = 51/60 = 17/20
A group of 200 people were asked which city they would like to visit next.
The table shows the results.
(a) A person from the group is chosen at random.
Write down the probability that this person would like to visit either Paris or Tokyo next.
(b) Two people are chosen at random from the group of 200.
Find the probability that one person would like to visit London next and the other person would like to visit New York next.
Give your answer as a percentage.
▶️ Answer/Explanation
(a) Ans: \(\frac{94}{200}\) (or simplified: \(\frac{47}{100}\))
From the table, number of people who prefer Paris = 50, Tokyo = 44.
Total for Paris or Tokyo = \(50 + 44 = 94\).
Probability = \(\frac{94}{200} = \frac{47}{100}\).
(b) Ans: 14.07%
From the table, number of people who prefer London = 62, New York = 45.
Number of ways to choose 1 London and 1 New York visitor = \(62 \times 45 = 2790\).
Total ways to choose any 2 people = \(\binom{200}{2} = \frac{200 \times 199}{2} = 19900\).
Probability = \(\frac{2790}{19900} \approx 0.1407\) or \(14.07\%\).