 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/b/ii/solution

Success after two draws occurs on the two mutually exclusive events

GR

and

RG

. With

N = g + r

P (GR) + P (RG) = \frac{g}{N} \frac{r}{N - 1} + \frac{r}{N} \frac{g}{N - 1} = \frac{2 g r}{N ( N - 1 )} .

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