Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at least 10, 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 rolls is at least 10 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.