Chen has three boxes. Box A contains 5 counters, of which 3 are white and 2 are yellow. Box W contains 4 red marbles and 3 blue marbles. Box Y contains 5 red marbles and 3 blue marbles. Chen chooses one counter at random from box A. If the counter is white, he chooses two marbles from box W, at random and without replacement. If the counter is yellow, he chooses two marbles from box Y, at random and without replacement.

Q: What topic does this question test?

This question tests Probability and statistics in A-Level Mathematics (syllabus code 9709). It is worth 8 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics Oct/Nov 2025 examination, Paper 5 Variant 3 (9709_w25_qp_53.pdf).

Question

Chen has three boxes. Box A contains 5 counters, of which 3 are white and 2 are yellow. Box W contains 4 red marbles and 3 blue marbles. Box Y contains 5 red marbles and 3 blue marbles. Chen chooses one counter at random from box A. If the counter is white, he chooses two marbles from box W, at random and without replacement. If the counter is yellow, he chooses two marbles from box Y, at random and without replacement.

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