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 P1A2, P1B2, P1A ∪ B2, P1Ac2, and P1A ¨ B2 by summing the probabilities of the appropriate sample points.

c. Use the additive rule to find P1A ∪ B2. Compare your answer with the one you obtained in part b.

d. Are the events A and B mutually exclusive? Why?