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