Thread: A tricky odds question URGENT

In the king of fighters 2 tournament, Goku and Vegeta are the final 2 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.?

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: .

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