A Seven Game Series


The probability that the NL wins in 7 games = P(NL wins exactly 3 out of the first 6 games) P(NL wins the seventh game) = (0.3125)(0.5000) = 0.15625

Games 1-6

(order does not matter)

Game 7

P(NL wins exactly 3 of 6 games) = C[6,3][(1/2)^3][(1/2)^3] = [(654)/(321)](1/8)(1/8) = (20)(1/8)(1/8) = 20/64 = 0.3125
P(NL wins) = 1/2 = 0.5000


The probability that the AL wins in 7 games = P(AL wins exactly 3 out of the first 6 games) P(AL wins the seventh game) = (0.3125)(0.5000) = 0.15625

Games 1-6

(order does not matter)

Game 7

P(AL wins exactly 3 of 6 games) = C[6,3][(1/2)^3][(1/2)^3] = [(654)/(321)](1/8)(1/8) = (20)(1/8)(1/8) = 20/64 = 0.3125
P(AL wins) = 1/2 = 0.5000


The probability that the series ends in 7 games =
P(NL wins in 7 games) + P(AL wins in 7 games) = 0.15625 + 0.15625 = 0.3125


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