Let A, B and C be events in a sample space S such that A ∩ C = 0 and A ∪ B ∪ C = S. If it is known that P(A) = .20, P(B) = .61, P(A ∪ B) = .75 and P(B ∩ C) = .10, find: (a) P(A ∩ B); (b) P(C ∩ B′ ). (c) Are A and B independent? Are A and C independent?

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