A Five Game Series


The probability that the NL wins in 5 games = P(NL wins exactly 3 out of the first 4 games) P(NL wins the fifth game) = (0.2500)(0.5000) = 0.1250

Games 1-4

(order does not matter)

Game 5

P(NL wins exactly 3 of 4 games) = C[4,3][(1/2)^3](1/2) = [(432)/(321)](1/8)(1/2) = (4)(1/8)(1/2) = 1/4 = 0.2500
P(NL wins) = 1/2 = 0.5000


The probability that the AL wins in 5 games = P(AL wins exactly 3 out of the first 4 games) P(AL wins the fifth game) = (0.2500)(0.5000) = 0.1250

Games 1-4

(order does not matter)

Game 5

P(AL wins exactly 3 of 4 games) = C[4,3][(1/2)^3](1/2) = [(432)/(321)](1/8)(1/2) = (4)(1/8)(1/2) = 1/4 = 0.2500
P(AL wins) = 1/2 = 0.5000


The probability that the series ends in 5 games =
P(NL wins in 5 games) + P(AL wins in 5 games) = 0.1250 + 0.1250 = 0.2500


Return to the analytical solution.

Or go straight to the explanation page for a 6 game series.