Jack and Jill run up the hill. The probability of Jack reaching the top first is p, while that of Jill is q. They decide to have a tournament, the grand winner being the first one who wins 3 races....

Jack and Jill run up the hill. The probability of Jack reaching the top first is p, while that of Jill is q. They decide to have a tournament, the grand winner being the first one who wins 3 races. Find the probability that Jill wins the tournament. Assume that there are no ties (p + q = 1) and that the races are independent.