 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/10/b/solution

p + q > 0

P (M ∣ S) = \frac{P ( S ∣ M ) P ( M )}{P ( S )} = \frac{p}{p + q} .

p = q = 0

, singing has probability zero and the stated observation cannot occur in this model; that conditional probability is undefined.

 New to topics? Read the docs here!