 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/iii/solution

The good and defective cases are disjoint and exhaustive. The law of total probability therefore gives

P (x_{0}) = p g_{0} + (1 - p) d_{0} .

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