Suppose the National League team has a probability of of winning a World Series game and the American League team has a probability of . The series is over as soon as one team wins four games. Find the probability that the series is over in seven games.
A) 0.1518
B) 0.2718
C) 0.1318
D) 0.1438
E) 0.1294

Question

Suppose the National League team has a probability of  of winning a World Series game and the American League team has a probability of  . The series is over as soon as one team wins four games. Find the probability that the series is over in seven games. ​
A) 0.1518 
B) 0.2718 
C) 0.1318 
D) 0.1438 
E) 0.1294

Quizplus · Accepted Answer

The series can only end in 4, 5, 6, or 7 games. The only way for it to end in exactly 7 games is if each team wins 3 games in the first 6 games, and then the 7th game determines the winner. The probability of this happening is:
(6 choose 3)(0.11)^3(0.89)^3(0.11) = 0.1318 (rounded to four decimal places)

Suppose the National League Team Has a Probability of