Anne and Bob play a game where they take turns rolling a pair of fair six-sided dice, and compute the product of the two numbers that turn up. Anne wins if, on her turn only, the product from her roll is divisible by 3. Bob wins if, on his turn only, the product from his roll is divisible instead by 2. A player cannot win on the other person's roll. They keep taking turns rolling the dice until one person wins. Anne rolls first.

(a) What is the probability that Anne wins?

(b) Given that Anne won on her second roll, what is the probability that neither dice ever turned up a "3" in those three rolls (two rolls by Anne, one roll by Bob)?