In a world series, terms A and B play until one team has won four games. Assume that each game played is won by team A with probability p, independently of all previous games,
a) for g = 4 through 7 find a formula in terms of p and q = 1 -p for the probability that team A wins in g games.
b) What is the probability that team A wins the world series, in terms of p and q?
c) Use your formula to evaluate this probability for p = 2/3.
d) Let X be a binomial (7, P) random variable. Explain why P(A wins) = P(X > 4) using an intuitive argument. Verify algebraically that this is true.
e) Let G represent the number of games played. What is the distribution G? For what value of P is G independent of the winner of the series?