Two individuals A and B, are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Suppose that the outcomes of successive games are independent, with P(A wins)=.3, P(B wins)

=.2, and P(draw)=.5. Each time a player wins a game he earns one point and opponent earns none. No points are given to either player for a draw. The first player to win five points wins the championship.

a) What is the probability that A wins the championship in just five games?

b) What is the probability that it takes just five games to obtain a champion?