 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/12/e/iii/solution

There are two equally likely balls bearing label eight, one of each colour. The conditional probability that the removed ball was green is therefore

1/2

P (second green ∣ X_{1} = 8) = \frac{1}{2} \frac{9}{19} + \frac{1}{2} \frac{10}{19} = \frac{1}{2} .

Both possible first colours must be included because the observed label alone does not determine the colour.

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