 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/16/a/ii/solution

Interchanging the two colours preserves the probability distribution when their population counts are equal. Thus the probability of two black balls is also

p_{w}

. The three mutually exclusive possibilities are two white, two black, or different colours, so

p_{d} = 1 - 2 p_{w} .

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