Hey

If the odds in favor 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?

Can someone give me an answer with explanation Plz.

Thanx

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- April 19th 2008, 07:20 PMballin_sensationProbabilities Plz Help
Hey

If the odds in favor 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?

Can someone give me an answer with explanation Plz.

Thanx - April 19th 2008, 08:38 PMSoroban
Hello, ballin_sensation!

Quote:

If the odds in favor 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?

There are three ways in which she can win three games.

(1) She wins the first three games:

. . .

(2) She wins two of the first three games, then wins the fourth game.

. . .

(3) She wins two of the first four games, then wins the fifth game.

. . .

Therefore: .

- April 19th 2008, 08:48 PMTheEmptySet
This seems like a binomial probabilility so

the prob of x successes in n trials is

where P is the prob of success

since we want an upset victory she needs to win 3,4, or 5 games

so we can add P(3) +P(4)+P(5) or take 1 -P(0)-P(1)-P(2)

Now lets set up the formula:

The odds are 5 to 4 against her so

and they are playing the best of 5 so

so P(3)+P(4)+P(5) - April 19th 2008, 08:49 PMTheEmptySetDang!
Too slow HAHA(Rofl)

- April 20th 2008, 07:23 AMballin_sensation
Thanx for the help guys, really appreciate it.