Let A, B, C be three events with P(A) = P(B) = P(C) = %. We assume that A and B are mutually exclusive and C is independent of both A and B. [3 marks] (a) Find P((A U B) n C). [2 marks] (b) Is A U B independent of C? Why? [3 marks] (b) Let X be the indicator random variable of the event (A U B) and Y the indicator random variable of the event (B U C) (that is, X = 1 if A U B occurred and 0 otherwise, Y = 1 if B U C occurred and 0 otherwise). Find the joint probability function of X and Y