I can only try-
I would use the binomial distribution to solve this.
To win in 4 games the Phillies need to win 4 games in a row, with a .50 chance of winning each game the probability of winning 4 in a row is .5^4 = .0625. (You can also use the binomial distribution but that is overkill for this case.)
To win in 5 games the Phillies need to win exactly three out of the first four games and game number five. The probability is (4 nCr 3) * (.5^3) * (.5^1) * .5 = 4 * .5^5 = .125.
To win in 6 games the Phillies need to win exactly three out of the first five games and game number six. The probability is (5 nCr 3) * (.5^3) * (.5^2) * .5 = 10 * .5^6 = .15625.
To win in 7 games the Phillies need to win exactly three out of the first six games and game number seven. The probability is (6 nCr 3) * (.5^3) * (.5^3) * .5 = 20 * .5^7 = .15625 (as above).
P(Winning in 4 or 5 games) = .0625 + .125 = .1875 = 18.75%
P(Winning in 6 or 7 games) = .15625 + .15625 = .3125 = 31.25%
So there is a much better chance that they will win in 6 or 7 games.
Please take note that 18.75% + 31.25% = 50% since each team has an equal chance of winning.
Using Excel, copy this table to a spreadsheet, the “3” should be in Cell A1:
3 =BINOMDIST(3,A1,0.5,FALSE) =B1*0.5
4 =BINOMDIST(3,A2,0.5,FALSE) =B2*0.5
5 =BINOMDIST(3,A3,0.5,FALSE) =B3*0.5
6 =BINOMDIST(3,A4,0.5,FALSE) =B4*0.5
If you’re not familiar with the binomial distribution please let me know.
(Can I suggest what type of soda to get.)