Question

The Yankees are playing the Dodgers in a world series. The Yankees

win each game with probability .6. What is the probability that the

Yankees win the series? (The series is won by the first team to win 4

games.)

Answer 1

There will be a total of 7 games in MLB world series and a team wins the series if it first wins 4 games of the series and also if a team wins the series without playing all the seven games then the leftover games are omitted.

Probability of Yankees winning a game = 0.6

Yankees will win the series if it wins 4 games in the played 4 games or 4 games in played 5 games or 4 games in played 6 games or 4 games in played 7 games

X be the number of games Yankees win in N games played

X follows a binomial distribution with parameters N and p = 0.6

Probability of Yankees winning the series = P(X=4;N=4) + P(X=4;N=5) + P(X=4;N=6) + P(X=4;N=7)

where x = 0,1,2,.....N

The probability that Yankees win the series = 0.99