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

A: {You will roll a 7 (i.e., the sum of the numbers of dots on the upper faces of the two dice is equal to 7).}

B: {At least one of the two dice is showing a 4.}

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

b. Find P(A), P(B), P(A B), P(A  B), and P(Ac) and by summing the probabilities of the appropriate sample points.

c. Use the additive rule to find P(A  B) . Compare your answer with that for the same event in part b.

d. Are A and B mutually exclusive? Why?