 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/11/a/solution

Let

C

mean control-group membership and

E

the adverse event. Equal allocation gives

P (C) = P (C^{c}) = 1/2

P (E) = (p_{0} + p_{1}) /2

P (C ∣ E) = \frac{p _{0} P ( C )}{p _{0} P ( C ) + p _{1} P ( C ^{c} )} = \frac{p _{0}}{p _{0} + p _{1}} .

This is defined when

p_{0} + p_{1} > 0

. If both are zero, the conditioning event has zero probability and the stated conditional probability is undefined.

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