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Probability: Defective Parts

  1. May 19, 2014 #1
    1. The problem statement, all variables and given/known data

    A manager must assess the quality of a new batch of 25 components ready for shipping.
    Rather than assess each component, a sample of 5 is randomly selected and tested. The
    quality control speci fication is that if there are 2 or more defectives in the sample, the
    quality manager must reject the batch. Suppose there are actually 3 defective components
    in this batch of 25.

    What is the probability that the batch is rejected?

    2. Relevant equations



    3. The attempt at a solution

    So I'm looking for the probability that 2 or 3 defective parts are taken in the sample of 5. I'm having trouble wrapping my head around the problem a bit.

    I said the probability of choosing all 3 is:

    (3/25).(2/24).(1/23)=1/2300

    What's confusing me is that this has only three picks when there's five parts picked in the sample. Am I missing something here? Any help would be much appreciated.
     
  2. jcsd
  3. May 19, 2014 #2

    LCKurtz

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    You have 3 bad and 22 good in the batch. If x is the number of bad, how many ways can you pick x out of the bad and 5-x out of the good? Have you studied the hypergeometric distribution yet?
     
    Last edited: May 19, 2014
  4. May 20, 2014 #3
    This is a sample exam question yes so I would've done hypergeometric distribution yes. I just don't quite understand how to use it so I never thought that's what this problem was.

    I think I know now when it should be used though. So:

    P(X=2)+P(X+3)

    P(X=2)=[(mCk).(N-m)C(n-k)]/(25C5)

    where N=25, m=3, k=2, n=5 and use the same approach for P(X=3) except k=3.

    Is this how the problem is done?
     
  5. May 20, 2014 #4

    LCKurtz

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    That's the idea.
     
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