Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 3 / 9H / iii

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- Solution iii

Solution

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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