@sonpham,
If in part (b), you want the probability of A winning a match of any length (call it P), then it can be solved recursively with:
P = p^2 + 2p(1-p)P
which works out to:
P = p^2 / (2p^2 - 2p + 1)
p^2 is the probability that A wins the first two games and ends the match.
2p(1-p) is the probability that they split the first two and, essentially, start over (which is why it is multiplied by P).