At Wimbledon, men's singles matches are played on a best of five sets basis, that is, players A and B play until one them has won 3 sets. Suppose each set is won by A with probability p, independently of all previous sets.
a) For each i = 3, 4, 5, find a formula in terms of p and q = 1 - p that player A wins in exactly i sets.
b) In terms of p and q, what is the probability that player A wins the match?
c) Given that player A won the match, what is the probability (in terms of p and q that the match tasted only three sets?
d) Compute the probability in c) for the case p = 2/3,
e) Do you think the assumption of independence made above is reasonable?