A Six Game Series


The probability that the NL wins in 6 games = P(NL wins exactly 3 out of the first 5 games) P(NL wins the sixth game) = (0.3125)(0.5000) = 0.15625

Games 1-5

(order does not matter)

Game 6

P(NL wins exactly 3 of 5 games) = C[5,3][(1/2)^3][(1/2)^2] = [(543)/(321)](1/8)(1/4) = (10)(1/8)(1/4) = 10/32 = 0.3125
P(NL wins) = 1/2 = 0.5000


The probability that the AL wins in 6 games = P(AL wins exactly 3 out of the first 5 games) P(AL wins the sixth game) = (0.3125)(0.5000) = 0.15625

Games 1-5

(order does not matter)

Game 6

P(AL wins exactly 3 of 5 games) = C[5,3][(1/2)^3][(1/2)^2] = [(543)/(321)](1/8)(1/4) = (10)(1/8)(1/4) = 10/32 = 0.3125
P(AL wins) = 1/2 = 0.5000


The probability that the series ends in 6 games =
P(NL wins in 6 games) + P(AL wins in 6 games) = 0.15625 + 0.15625 = 0.3125


Return to the analytical solution.

Or go straight to the explanation page for a 7 game series.