A black and a red dice are rolled. Find the conditional

Solution

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