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February 26th, 2012, 03:46 PM   #1
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Odds of Event Y, X number of times

Let's say the chance of being blue-eyed is 5%. Let's say there's a group of twenty people. Using this group, what are the odds that X are blue-eyed, 5 blue-eyed, or 18 blue-eyed?
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February 26th, 2012, 07:38 PM   #2
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Re: Odds of Event Y, X number of times

Are you working on binomials? That equation is:



The equation is not as nasty as it looks. Your n is 20. x will be whatever value you are looking for out of the 20 people. p = .05 as given in the problem. 1-p is exactly what it says (sometimes called q), and is the probability of not being blue-eyed. The n-x is also exactly what it says.

You can plug n chug that, but a little explanation:

You're taking the probability of the "success" (being blue-eyed) and multiplying it the number of times you want the success (like 5). But that leaves (n-x) for the number of "failures" (not being blue-eyed), so you multiply the (1-p) the number of times that would be a failure. (5 blue-eyed means 15 non-blue-eyed). Don't take the success/failure thing too seriously - it just means the ones you're looking for (blue-eyed) versus the ones you aren't looking for (non-blue-eyed).

Then we have to take all that and multiply by how many ways there are to pick those 5 blue-eyed people out of the 20 total, hence the combination.

If you're not sure how to go through and solve that equation, ask what you don't understand. If you're not doing binomials, um, well, I guess say so.
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February 29th, 2012, 12:33 PM   #3
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Re: Odds of Event Y, X number of times

Thank you! I'm not in school so this isn't a homework problem. I just thought about it and wanted to figure it out, then realized it's harder than just multiplying fractions.

Can you recommend a free calculator I can download and plug all this into?
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February 29th, 2012, 12:51 PM   #4
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Re: Odds of Event Y, X number of times

Ohhh! Binomial distributions. Fun.

You can use wolframalpha.com, or if you have access to Mathematica or purchase it, it's a very powerful mathematics tool
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March 1st, 2012, 12:53 AM   #5
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Re: Odds of Event Y, X number of times

Quote:
Originally Posted by andytx
Thank you! I'm not in school so this isn't a homework problem. I just thought about it and wanted to figure it out, then realized it's harder than just multiplying fractions.
You're welcome. And... it's mostly multiply fractions: 5/100 and 95/100.
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