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February 26th, 2012, 03:46 PM  #1 
Newbie Joined: Feb 2012 Posts: 2 Thanks: 0  Odds of Event Y, X number of times
Let's say the chance of being blueeyed is 5%. Let's say there's a group of twenty people. Using this group, what are the odds that X are blueeyed, 5 blueeyed, or 18 blueeyed?

February 26th, 2012, 07:38 PM  #2 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  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. 1p is exactly what it says (sometimes called q), and is the probability of not being blueeyed. The nx 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 blueeyed) and multiplying it the number of times you want the success (like 5). But that leaves (nx) for the number of "failures" (not being blueeyed), so you multiply the (1p) the number of times that would be a failure. (5 blueeyed means 15 nonblueeyed). Don't take the success/failure thing too seriously  it just means the ones you're looking for (blueeyed) versus the ones you aren't looking for (nonblueeyed). Then we have to take all that and multiply by how many ways there are to pick those 5 blueeyed 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. 
February 29th, 2012, 12:33 PM  #3 
Newbie Joined: Feb 2012 Posts: 2 Thanks: 0  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? 
February 29th, 2012, 12:51 PM  #4 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  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 
March 1st, 2012, 12:53 AM  #5  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Odds of Event Y, X number of times Quote:
 

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