2. Suppose that A and B are two events, defined on a sample space , with P(A) = 0.23, P(B) = 0.32. (a) In the case when A and B are mutually exclusive find P(An B) and P(A U B). (b) Can A C B? If so find P(An B) and P(AU B). If not explain why not? (c) Can B C A? If so find P(An B) and P(AU B). If not explain why not? (d) Is it possible that P(A UB) = 1? Explain why or why not. (e) Is it possible that P(An B) = 0? Explain why or why not. (f) In the case when A and B are independent find: i. P(A| B) ii. P (B| AC)