Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, , E7 denote the sample points. The following probability assignments apply: P(E1) = 0.15, P(E2) = 0.20, P(E3) = 0.05, P(E4) = 0.25, P(E5) = 0.10, P(E6) = 0.20, and P(E7) = 0.05. Let A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}. (a) Find P(A), P(B), and P(C). P(A) = P(B) = P(C) = (b) Find A ∪ B. (Enter your answer in set notation.) A ∪ B = Find P(A ∪ B). P(A ∪ B) = (c) Find A ∩ B. (Enter your answer in set notation.) A ∩ B = Find P(A ∩ B). P(A ∩ B) = (d) Are events A and C mutually exclusive? They mutually exclusive. (e) Find BC. (Enter your answer in set notation.) BC = Find P(BC). P(BC) =