1. (a) [10 pts] Suppose Al, A2, A3 are events such that P(A, n A2) = P(An Ag) # 0 while P( A2 n A3) = 0. Calculate the probability that at least one of these events occurs by calculating P(A] U A2 U A3) in terms of only P(Al), P(A2), P(A3) and P(Ain A2). (b) [5 pts] If A1, A2, A3 are pairwise independent events is it possible that P(A] n A2) = P(AIn As) # 0 while P(A2 n A3) = 0, and what does it say about the events Al, A2, Ag? You have to justify your answer with a calculation