 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability/8/a/ii/solution

Let

D

denote the selected die. Bayes' theorem gives

P (D = 1 ∣ X = 1) = \frac{P ( X = 1 ∣ D = 1 ) P ( D = 1 )}{P ( X = 1 )} = \frac{( 1/2 ) ( 1/6 )}{1/6} = \frac{1}{2} .

Only the first roll is conditioned on here; the second outcome has not been observed.

 New to topics? Read the docs here!