 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/14/a/iv/solution

Divide the relevant joint probability by the marginal stopping probability. By Bayes' theorem,

P (D ∣ x_{1}) = \frac{( 1 - p ) d _{1}}{p g _{1} + ( 1 - p ) d _{1}} .

The denominator is positive under the stated assumptions.

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