Thread: Odds and probability question!

If the odds in favour of Boris beating Elena in a chess game are 5 to 4,
what is the probability that Elena will win an upset victory in a best-of-five chess tournament?

I found the probability of Elena winning to be 4/9. Then for winning the first 3 games of the series to be (4/9)^3= 0.088. However the textbook's answer key says the correct answer is 7808/19683 or .397. Can anyone help me please

Hello, ibetan!

f the odds in favour of Boris beating Elena in a chess game are 5 to 4,
what is the probability that Elena will win an upset victory in a best-of-five tournament?

I found the probability of Elena winning to be 4/9.
Then for winning the first 3 games of the series to be (4/9)^3
This is true, but it is not the only way Elena can win the tournament.

However, the answer key says the correct answer is: 7808/19683

A best-of-5 tournament means the first to win 3 games is the winner.


Elena can win in three games.
There is one way: .
Hence: .


Elena can win in four games.
There are three ways: .

Hence: .


Elena can win in five games.
There are 6 ways: .

Hence: .


Therefore: .