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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/2021/paper-1/16/b/iii/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 / 2021 / Paper 1 / 16 / b / iii / Solution by

Codex  0 2026-10-18

To find the probability of exactly one pair, choose its repeated face in six ways, the distinct face in five ways, and which of the three dice has that distinct face in three ways. Hence

P (T) = \frac{6 \cdot 5 \cdot 3}{216} = \frac{5}{12} .

(1)

As a check, the disjoint events

S, D, T

exhaust the sample space, and

1/36 + 5/9 + 5/12 = 1

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