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Statistics: Tolerances

  1. Feb 18, 2014 #1
    1. The problem statement, all variables and given/known data

    What is the probability that among a collection of 20 assemblies we have exactly 2 loose-fits and 1 interference fits?

    P(loose-fit) = .1335
    P(Interference fit) = .083

    2. Relevant equations



    3. The attempt at a solution

    I am thinking that I just add the two binomial distributions together.

    P(Loose = 2) = (20 choose 2)*.1335^2 * (1-.1335)^18
    +
    P(Interference = 1) = (20 choose 1)*.083^1 * (1-.083)^19

    This comes out to: .25677 + .31998 = .57675

    But, I feel like I am missing something. Anyone that can confirm or deny will be much appreciated!
    Thanks!
     
  2. jcsd
  3. Feb 19, 2014 #2
    Just in case anyone comes across this in the future. It is done by using the multinomial distribution. Apparently the binomial is a generalization of the multinomial with k=2. Good to know.
     
  4. Feb 19, 2014 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    It exactly opposite to what you say: the multinomial is a generalization of the binomial, and not the other way round.
     
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