 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-3/9h/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

During any year, repeats may be ignored until the first non-repeat outcome. Conditional on that event, the chance of progressing is

\frac{r}{p + r} = \frac{r}{1 - q} .

The student must progress successfully through all three years. By the Markov property, the required probability is therefore

(\frac{r}{p + r})^{3} .

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