A fair coin is tossed three times, and the events A and B are defined as follows:
A: {At least one head is observed.}
B: {The number of heads observed is odd.}
a. Identify the sample points in the events A, B, A ⋃ B, Ac, and A ∩ B.
b. Find P(A), P(B), P(A ⋃ B), P(AC), and P(A ∩ B) by summing the probabilities of the appropriate sample points.
c. Find P(A ⋃ B) using the additive rule. Compare your answer to the one you obtained in part b.
d. Are the events A and B mutually exclusive? Why?