In a MLB championship series the team who wins four out of s

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

Solution

a) X is binomial with n = 7 and p = 0.55

PMF of x

= P(X=r) = 7Cr(0.55)^r(0.45)^7-r, r=0,1,2,3,4,5,6,7

----------------------------

b) P(X=6) = 0.0872

c) P(X>=4) = 0.6083

d) P(X>=3) = 0.8471

To win the series two times should win.

As each series is independent

prob =0.8471²

= 0.7176