 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/i/solution

After one draw the two counts are either

(1, 0)

(0, 1)

and cannot agree. Therefore

P (success after one draw) = 0 .

This is the elementary parity restriction behind the first return time interpretation of this game.

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