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Math Help - Probability Question

  1. #1
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    Probability Question

    A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. If a defective item is found, the shipment of 10 items will be rejected.

    If a sample of 3 items is selected, what is the probability that the shipment will be rejected?

    I used f(x)=(nCr(2,x)*nCr(8,3-x))/nCr(10,3)
    f(1)=.466667

    Book answer is .5333333.

    Is the book right?
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  2. #2
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    Quote Originally Posted by lisakki View Post
    A shipment of 10 items has two defective and eight nondefective items. In the inspection of the shipment, a sample of items will be selected and tested. If a defective item is found, the shipment of 10 items will be rejected.

    If a sample of 3 items is selected, what is the probability that the shipment will be rejected?

    I used f(x)=(nCr(2,x)*nCr(8,3-x))/nCr(10,3)
    f(1)=.466667

    Book answer is .5333333.

    Is the book right?
    I haven't done any calculations but I'll make a bet with you ....

    If X is the random variable number of defectives in sample, I'll bet that you only calculated Pr(X = 1) rather than \Pr(X \geq 1), which is equal to 1 - Pr(X = 0) by the way.
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  3. #3
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    Hypergeometric Problem

    Hi:
    This is a hypergeometric problem! N=10 n1=2 and n2=8 and the Probability=1-(2C0)*(8C3)/(10C3). Because if one defective component is found, the shipment will be rejected. You only need to concern about there is no defective component is found, and then use 1 minus the answer. The book answer is correct.
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