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A-LevelMathematicsProbability and statistics9709/53 · May/June 2020 · Q24 Marks

In a certain large college, 22% of students own a car.

(a)3 students from the college are chosen at random. Find the probability that all 3 students own a car.[1]
(b)16 students from the college are chosen at random. Find the probability that the number of these students who own a car is at least 2 and at most 4.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B1] 0.22^3 = 0.0106
[M1] P(2, 3, 4) = 16C2 0.22^2 0.78^14 + 16C3 0.22^3 0.78^13 + 16C4 0.22^4 0.78^12
[A1] 0.179205+0.235877+0.216221
[A1] 0.631

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About this question

Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2020 Paper 5 Variant 3, question 2.

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