 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-2/9f/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

The two possible ways to observe one ball of each colour have probabilities

P (W_{I}, B_{II}) = \frac{3}{5} \frac{3}{4} = \frac{9}{20}, P (B_{I}, W_{II}) = \frac{2}{5} \frac{1}{4} = \frac{2}{20} .

Conditioning on their union therefore gives

P (W_{I}, B_{II} ∣ one white and one black) = \frac{9}{11} .

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