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] = [(6·5·4)/(3·2·1)]·(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] = [(6·5·4)/(3·2·1)]·(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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