Five-Game Series

Two basketball teams meet in the final round of a tournament.  The format is a best-of-five series.  The two teams are evenly matched, but the team playing at home has a 60% chance of winning.  The site format is H-H-A-A-H, where H indicates a home game and A indicates an away game.  To keep track of the teams, let’s call the team that starts the series at home the Yellow Jackets, and their opponent the Polar Bears.

a) What is the probability that the series is decided after first three games (one team sweeps)?

b) What is the probability that the series goes the full five games?

c) When the series is decided in four games, what is the probability that the Polar Bears won?