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Deriving the binomial distribution formula

  1. Jun 10, 2010 #1
    I am trying to follow along with this derivation of the binomial distribution formula:
    b(x;n,p) = nCx*pxqn-x

    But I do not really understand the meaning of the part on bold. What is this "specified order" business now? I feel like I am missing something big here.

     
  2. jcsd
  3. Jun 10, 2010 #2
    Think about what the "nCx" part of the formula does.

    Let's say we're rolling a regular dice 4 times, and we want the probability of a 6 only once. We know this would consist of 1 success and 3 failures ( [tex]\frac{1}{6}\frac{}{}[/tex] )( [tex]\frac{5}{6}[/tex] )3, however it does not account for which roll we get the 6, since it can occur in any 1 out of the 4 rolls, we multiply by 4C1.

    So that "specific order" business is to eliminate the need to account for exactly when our successes occur

    Does that make sense?
     
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