 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/18/b/solution

Insert the values from (a) into Bayes' theorem:

\frac{P ( A ∣ B ) P ( B )}{P ( A )} = \frac{( 4/5 ) ( 5/9 )}{13/18} = \frac{8}{13} = P (B ∣ A) .

Thus the identity is satisfied. Equivalently, both

P (A ∣ B) P (B)

and

P (B ∣ A) P (A)

equal the joint probability

4/9

 New to topics? Read the docs here!