Hello, KelvinScale!

Two baseball teams play a best-of-seven series

in which the series ends as soon as one team wins four games.

The first two games are played on A's field, the next 3 on B's and the last 2 on A's.

Given that the probability A wins on their home field is 0.7, and on B's field is 0.5,

what is the probability the series does not go to 6 games?

There is no formula for this problem.

I had to make a brute-force LIST of the possible outcomes.

Suppose wins the series.

could win the first four games: .

could win 3 of the first 4 games, then win the 5th game.

. .

Hence: .

. . . . . . . . . .

Suppose wins the series.

could win the first four games: .

could win 3 of the first 4 games, then win the 5th game.

. .

Hence: .

. . . . . . . . . .

Therefore: .