Suppose that the two soccer teams, the Juniors, and the Seniors, play a series of games. Assume that the results of these games are independent and that the Juniors have a 0.54 probability of winning each game. Let W = a win for the Juniors and L = a loss for the Seniors. a) What does it mean to say that the reSults of the games are independent? b) What is the probability that the Juniors win zero games in the rst three series to the game? e) What is the probability that the Juniors win the rst three games of the series? d) What is the probability that the Juniors win two games before the Seniors win two games? e) Suppose that Junior's probability of winning each game was larger than 0.54. Would this increase, decrease, or not change the probability that the Juniors win two games before the Seniors win two games? f) Suppose you want the Juniors to win the series of games against the Seniors. Would you prefer the series to be a single game, a best of three series, or a best of ve senes? g) If a series of 6 games are played, how many games are the Juniors expected to win? Explain what distribution you can use to model the Juniors wins and expected value. h) Let X be the number of games that the Seniors must play up to and including their rst win. What is the probability that the Seniors win their rst game on the fourth game in the series? What is the expected number of games the Seniors must play before they win their rst game