A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

Let the first observation be from the black die and second from the red die. When two dice (one black and another red) are rolled, the sample space S = 6 × 6 = 36 Now, A : obtaining a sum greater than 9 = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} B: Black die results in a 5. = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)} Therefore, (A ∩ B) = {(5, 5), (5, 6)} The conditional probability of obtaining a sum greater than 9, given by the black die resulting in a 5, is given by P( A|B). Therefore, P(A|B) = P(A ∩ B)/ P(B) = (2/36)/(6/36) = 2/6 = 1/3