Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be the event that the first one is a multiple of 3.

Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be the event that the first one is a multiple of 3.

(a) What is the probability that the sum of the two dice is 8 given that the first one is a multiple of 3? Show all work. Just the answer, without supporting work, will receive no credit.

(b) Are event A and event B independent? Explain.