Suppose that two evenly matched teams (say team A and team B), each with probability.5 of winning any given game, make it to the baseball World Series. The series ends assoon as one of the teams has won four games. Thus, it can end as early as the 4 th game (a"sweep") or as late as the 7 th game, with one team winning its fourth game after havinglost three of the ?rst six games.
a) Calculate the probability that the series ends in 4 games,5 games, 6 games, or 7 games.
b) What is the expected value of X , the number of games ittakes to complete the series?
c) Repeat (a) and (b) under the assumption that team A will win a given game with probability .6
d) Suppose team A will play up to four games on its home ?eld (game 1, 2,6, and 7, the 5 th , 6 th , 7 th games played only "if necessary"). The other games (game 3, 4,and, if necessary, game 5) will be played on Team B's home ?eld. Assume that each team will win its home games with probability .6. What are that chances that team A wins the series?