You could run a simulation but the logic is follows. Assume that the probability a team wins a game remains constant throughout the series and that the games are independent. The probability that Cubs wins the series in 4 games is p = .55^4 since there is only one way to win 4 games, sweep the first 4. The probability Cubs wins the series in 5 games is p = .55^4*.45^1*(4!/(( 4 - 1)!*1!) There are 4 different ways to win 4 games in a 5 game series. Remember that cannot win games 1,2,3,4 or series is over in 4 games. The probability Cubs wins the series in 6 games is P(Cubs win in 6 games) = p = .55^4*.45^2*(5!/(( 5 - 2)!*2!) There are 10 different ways to win 4 games in a 6 game series. and the probability Cubx win the series in 7 games is P(Cubs win in 7 games) = p = .55^4*.45^3*(6!/(( 6 - 3)!*3!) There are 20 different ways to win 4 games in a 7 game series. The probability that A wins the series is then P (Cubs win the series) = sum( all probabilities above)
