In the MLB championship series, the team who wins four out of seven will be winner. Assume that the Phillies have probability 0.55 of winning over the Boston Red Sox and both teams will face each other in the 2009 championship games. Let X be the random variable that represents number of games x (trials) required for Phillies to win championship.
a) Write down the formula that represents the probability mass function of X
b) Determine the probability that the Phillies will repeat and win the series in six games?
c) Determine the probability that the Phillies will win the series?
d) Suppose that the probability that the Phillies will win in the playoffs Phillies remains 0.55, and the winner is decided by the winning three out of five games. One more time the Phillies will face the Mets, what is the probability that the Phillies will win the playoff series?