44 A pair of fair dice is tossed. Define the following events:

A: 5You will roll a 7 1i.e., the sum of the numbers of dots on the upper faces of the two dice is equal to 7).6 B: 5At least one of the two dice is showing a 4.6

a. Identify the sample points in the events A, B, A  B, A  B, and Ac.

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

c. Use the additive rule to find P1A  B2 . Compare your answer with that for the same event in part b.

d. Are A and B mutually exclusive? Why?