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Probability Question - Urn problem

  1. Mar 31, 2013 #1
    1. The problem statement, all variables and given/known data

    An urn contains 4 white and 4 black balls. We randomly choose 4 balls. IF 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again randomly select 4 balls. this continues until exactly 2 of the 4 chosen are white. What is the probability that we shall make exactly n selections.

    2. Relevant equations



    3. The attempt at a solution

    I don't see why I can't find the probability of drawing exactly 2 white balls using this method.

    (4C2)(4/8)^2(1-4/8)^2
    where 4C2 is 4 choose 2

    apparently this is wrong but I don't see why. Thanks for any help that you can provide.
     
  2. jcsd
  3. Mar 31, 2013 #2

    Dick

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    Well, why do you think it's right? The probability of choosing a white ball is only 1/2 the first time you choose a ball. It's not always 1/2, is it?
     
  4. Mar 31, 2013 #3
    oh i guess i always assumed you pick the things simultaneously as that's what I've been doing throughout the course so i guess this assumption is wrong?
     
  5. Mar 31, 2013 #4

    Dick

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    If you pick a white ball first that means there are 3 whites left and 4 blacks. The odds of picking a second white or a black aren't 1/2 anymore. So yes, it's wrong.
     
  6. Apr 2, 2013 #5

    Bacle2

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    I think it is always useful to describe the sample space: you can succeed the 1st, or the 2nd time, etc.

    EDIT: I mean, you can select the two balls in the first trial, or, if you don't, then at the second trial, etc.
     
    Last edited: Apr 2, 2013
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