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Math Help - hypergeometric question

  1. #1
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    hypergeometric question

    I'm having a little trouble with this question:

    A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) \geq 0.8?

    any hints would be helpful.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lllll View Post
    I'm having a little trouble with this question:

    A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) \geq 0.8?

    any hints would be helpful.
    Assume selection without replacement.

    P(n_{d} \ge 1|N)=1-P(n_{d} = 0|N)

    where we take a saple of size N

    So P(n_d=1|N)\ge 0.8 is the same as P(n_d=0|N) < 0.2

    P(n_d=0|N) =\frac{17}{20}\times \frac{16}{19} \times .. \times \frac{18-N}{21-N}

    Now construct a table of P(n_d=0|N) for N=1, 2, .. and find the smallest
    N such that P(n_d=0|N)<0.2.

    RonL
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