In the World Series of baseball two teams A and D play a seq

In the World Series of baseball, two teams A and D play a sequence of games against each other and the first team that wins a total of four games becomes the winner of the World Series. If the probability that team A will win any particular game against team B is 0.4. What is the probability that team A will win the World Series ? 0.4 0.6 0.2898 0.7102 0.3077

Solution

this is binomila distibruion.

x: number of games won

when 4 games are won, the team is the winner.

ssume that the teams play seven games

we need to find P(X>=4)=P(X=4)=P(x=5)+P(x=6)+P(x=7)

summing the p(x) values we get 0.2898

P(x=4)

x	p(x)
4	0.193536
5	0.077414
6	0.017203
7	0.001638