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 isthe only way Elena can win the tournament.not

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: .