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 = {E1, E4, E6}
B = {E2, E4, E7}
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($B^c$).
