Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at most 6, and B be the event that the first one is an...

Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at most 6, and B be the event that the first one is an even number.

1. (a)  What is the probability that the sum of the two rolls is at most 6 given that the first one is an even number? Show all work. Just the answer, without supporting work, will receive no credit.
2. (b)  Are event A and event B independent? Explain.