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Probability Calculation

  1. Sep 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose you flip 1000 coins, what is the probability of flipping exactly 500 heads and 500 tails. (Hint: First write down the formula for the total number of possible outcomes. Then, to determine the "multiplicity" of the 500-500 macro state, use stirlings approximation.



    2. Relevant equations



    3. The attempt at a solution

    I have done a couple of these problems (successfully) with the binomial distribution method so am I wrong in stating the following equality? Or is this correct and I should just use the stirlings method to make N!~ NlnN - N at large N and then use this to simplify the probability I wrote? Thanks!

    probability = (1000 choose 500)((.5)^500)*((.5)^500)
     
  2. jcsd
  3. Sep 17, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    It is correct. Stirling's formula will allow you to calculate that, yes.
    And WolframAlpha can do it as well.
     
  4. Sep 17, 2014 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Yes, that is correct. Notice also that ##.5^{500} \times .5^{500} = .5^{1000} = 1/2^{1000}##.
     
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