Hello, Faisal2007!

There is no neat formula for this problem.

We must list the possible outcomes . . .

In the "King of Fighters 2" tournament, Goku and Vegeta are the final two combatants

and must face each other in the main event.

The tournament winner is determined in a best-of-five-matches series.

If the odds of goku beating vegeta are 5 to 7,

what is the probability Goku will win the tournament?

We have: .

Three-match series: Goku wins the first three matches.

. . The probability is: .

Four-match series: Goku wins two of the first three and the fourth match.

. . There are three ways: .

. . The probability is: .

Five-match series: Goku wins two of the first four and the fifth match.

. . There are six ways: .

. . The probability is: .

Therefore: .

. . . . . . . . . . . . . . . . .