Let X and Y be two events such that P(X Y)= 1 2 , P(Y / X)= 1 3 and P(X Y)= 1 6 . Which of the following is (are) correct?

Step-by-step solution

P(X / Y)= P(X Y) P(Y) 1 2 = 1 / 6 P(Y) P(Y)= 1 3 Similarly, P (Y / X)= P(X Y) P(X) 1 3 = 1 / 6 P(X) P(X)= 1 2 (a) P(X Y)=P(X)+P(Y)-P(X Y)= 1 2 + 1 3 - 1 6 = 2 3 (a) is true. (b) P(X Y)=P(X) P(Y) X and Y are independent events. (b) is true. But (c) is not true. (d) P (X^ C Y )=P (X^ C ) P(Y)= 1 2 1 3 = 1 6 (d) is not true.