23. 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) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05. Let A 5 B 5 C 5

{E1, E4, E6}

{E2, E4, E7}

{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 Bc and P(Bc).