 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/10/a/solution

Let

S

denote singing, and

M, F

denote male and female. Equal population counts give

P (M) = P (F) = 1/2

P (S) = pP (M) + qP (F) = \frac{p + q}{2} .

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