23. Suppose that we have a sample space S = { E,, Ez, Ej. Ex. Es. Ec, E,), where E, E2. . . . . E, denote the sample points. The following probability assignments apply: P(E, ) = .05. P(E,) = .20, P(E;) = .20. P(E,) = .25, P(E,) = .15, P(E) = .10, and P(E,) = 05. Let A = (E,, E.. El C = \\ E,. Ex. Es. E,) a. Find P(A), P(B), and P(C). b. Find A U B and P(A U B). c. Find A () B and P(A n) B). d. Are events A and C mutually exclusive? e. Find B and P( B )