need solution problem 1,2,3

1. Let A, B and C be events in a sample space S such that An C = 0 and AU BUC = S. If it is known that P(A) = .20, P(B) = .61, P(AUB) = .75 and P(BnC) = .10, find: (a) P(An B); P (Cn B' ) . (c) Are A and B independent? Are A and C independent? 2. Recall that n! r!(n - r)!' Prove that for positive integers n and k with k 2 (a) Find the distribution function F(x). (b) Find P(1