Biased Bernoulli Process
Suppose that two teams that meet in the world series are closely matched: the better team wins a given game with a probability of .55. What is the probability that the better team will win the World Series? Treat the games as tosses of a biased coin. Express the event "the better team wins" in terms of elementary Bernoulli events, and then compute the probability. How long must a series of games be in order to be reasonably certain (with 95% probability) that the best team will win?