odds and probabilities: '3 to 5 in favor', '3/8 probability'

panaloca8

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Jul 27, 2006
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:( Well, I am obviously having problems with probabilities. I just want to know how an odd in favor of an event is 3 to 5 and then the probability of that event is 3/8. I am clueless. How does this odd equal that probability??

confucious :roll:
 
Three chances are "for"; five chances are "against". This adds to eight chances, three of which are favorable. In other words, a 3/8 probability of a favorable outcome.

Eliz.
 
Re: odds and probabilities: '3 to 5 in favor', '3/8 probabil

Hello, panaloca8!

Odds in favor of an event is 3 to 5, then the probability of that event is 3/8.
How does this odd equal that probability?

If your probability of winning is \(\displaystyle \frac{3}{8}\), then your probability of losing is \(\displaystyle \frac{5}{8}\)

Your ratio of wins-to-losses is: \(\displaystyle \,\frac{3}{8}\,:\,\frac{5}{8}\,\) or \(\displaystyle \,3\,:\,5\)

\(\displaystyle \;\;\)and that is your odds of winning.


Odds are used to ensure a "fair" bet.

If you were playing game in which you'd win only \(\displaystyle \frac{3}{8}\) of the time.
\(\displaystyle \;\;\)it would unwise (dumb!) to bet "even money" . . . right?

But if you put up $3 and they put up $5, the game would be "fair".
\(\displaystyle \;\;\)The expected value is $0 . . . Neither side would have an advantage.


 
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