 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-1/7/b/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

For

B

to make a first throw,

A

must first pass, with probability

1/2

. For

B

then to win on that throw,

B

must roll one of two winning faces, with probability

1/3

. The throws are independent, giving

P = \frac{1}{2} \frac{1}{3} = \frac{1}{6} .

A first throw of

3

A

would make

B

win without throwing, and is excluded by the requested event.

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