43 A fair coin is tossed three times, and the events A and B are defined as follows:

A: 5At least one head is observed.6 B: 5The number of heads observed is odd.6

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?