 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-2/11/b/iv/solution

By inclusion-exclusion, subtract the intersection once to correct the double counting:

P (E_{1} \cup E_{2}) = P (E_{1}) + P (E_{2}) - P (E_{1} \cap E_{2}) = \frac{2}{7} + \frac{2}{7} - \frac{1}{21} = \frac{11}{21} .

As a check, the complementary event is two greens, of probability

(5/7) (4/6) = 10/21

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