Problem 4 Two teams1 A and B , play a series of games. (a) If team A has probability 0.4 of winning each game, is it to its advantage to play the best 3 out of 5 games or the best 4 out of 7? Assume the outcomes of successive games are independent. (b) Suppose the game continues until team A wins its third game. Let N be the number of games played. Note that N has a negative binomial distribution. Find ll\"(N g 5) and show that it is equal to the rst probability calculated in part (a) (c) Assume as in (b). What is the probability that team A has to play at least 8 games before it beats team B three times