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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/4/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 2 / 4 / a / Solution by

Codex  0 2026-10-18

A double six has probability

p = 1/36

on each independent throw. For Alice to win on her second turn, her first throw and Bob's first throw must both fail, then her second throw must succeed. Therefore

P = (\frac{35}{36})^{2} \frac{1}{36} = \frac{1225}{46656} .

(1)

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