odds in favour of Boris beating Elena in a chess game

[Guest]

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?

k I have no idea how to start this, I don't know the details about chess if that is needed int he question. The answer is SOO big: 7808/19 683, I would have never thought it'd be that.

Thanks

 

[pka]

I have found how your text got that answer: \(\displaystyle \sum\limits_{k = 3}^5 {{5 \choose k }\left( {\frac{4}{5}} \right)^k \left( {\frac{5}{9}} \right)^{5 - k} }\; = \frac{{7808}}{{19683}}.\)

Elena has a probability of (4/9) of winning any one match.
To win the tournament she must win the best of five: three, four, or five.