 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-2/section-a/9/b/solution

Let

I_{1}, I_{2}

be indicator random variables for the two draws being red. Each draw has red probability

3/7

, even though the draws are dependent. By linearity of expectation, the number

R = I_{1} + I_{2}

satisfies

E [R] = \frac{3}{7} + \frac{3}{7} = \frac{6}{7} .

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