Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. For each game they play, the probability that the Bears win is 0.6 and the probability the Wildcats win is 0.4.
(a) What is the probability that the Bears win the series in exactly 3 games (i.e. only 3 games are required to finish the series and the Bears are the ones that win)?
(b) What is the probability that the Wildcats win the series in exactly 3 games?
(c) What is the probability that the Bears win the series in exactly 4 games?
(d) What is the probability that the Wildcats win the series in exactly 4 games?
(e) What is the probability that the Bears win the series in exactly 5 games?
(f) What is the probability that the Wildcats win the series in exactly 5 games?
(g) What is the probability that the Bears win the series (i.e. the Bears win but we don't care how many games are required)?
(h) What is the probability that the Wildcats win the series?