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Multiple Percentages Probability

  1. Sep 30, 2006 #1
    Hi, I seem to be having problems calculating this out. My friends were asking me how to caculate multiple precentages and I thought it would be easy but I got a little stuck. Here is the problem.

    Lets say there is a program that spits out the words yes and no. 60% chance it says yes and 40% chance it says no. If I hit it once, there is a 60% chance it says yes and a 40% chance it says no. If I click it 7 times and it says yes 6 times, what are the odds? I put .6^6 to calculate it, but it seems that I don't include the fact that it says no once. Also, what would the odds be if it said yes all 7 times or no all 7 times? How would you calculate these percentages?

    Thanks alot, seems like a great forum so far.
     
  2. jcsd
  3. Sep 30, 2006 #2

    CRGreathouse

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    You're looking for what's called the binomial distribution.

    The odds of exactly 6 out 7 "yes" is (7 choose 6) * 0.6^6 * 0.4 ^ 1. Let me explain. You are getting 6 "yes" and 1 "no"; the chances of getting those answers []in that order[/i] is 0.6^6 * 0.4 ^ 1. Since you don't care about the order, you need to multiply this by the number of ways to choose 6 elements out of 7. In general, (x choose y) is

    [tex]\frac{x!}{y!(x-y)!}[/tex]

    For (7 choose 6), that's 7!/(6! * 1!) = 7, giving a total probability of [itex]7\cdot0.6^6\cdot0.4^1[/itex].
     
  4. Sep 30, 2006 #3
    Thanks so much
    I cant believe someone actually solved this for me in such a clear manner.
    This forum is great!
     
  5. Sep 30, 2006 #4

    CRGreathouse

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    I'm glad to have helped. o:)
     
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