 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/17/c/ii/solution

B

and

\overline{B}

form a partition. The law of total probability therefore gives

P (A ∣ \overline{B}) P (\overline{B}) + P (B) P (A ∣ B) = P (A) .

As written, both conditionals require nonzero conditioning probabilities.

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