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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/16/a/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2020 / Paper 1 / 16 / a / ii / Solution by

Codex  0 2026-10-18

Condition on an apple occupying position two in a uniformly random ordering. The nine other positions then contain four apples and five bananas, each equally likely to occupy position three. The conditional probability is therefore

P (A_{3} ∣ A_{2}) = \frac{4}{9} .

(1)

This uses exchangeability of the unconditioned positions; there is no need to assume the first lunch contained a particular fruit.

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