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Math Help - Probability

  1. #1
    Junior Member BobBali's Avatar
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    Probability

    Question

    5% of all batteries produced are defective. Batteries are sold in packs of 4.

    1)What is the probability that a pack contains exactly 2 defective batteries?
    2)Atleast 1 is defective?

    My working

    P (def) = 0.05 P (not def) = 0.95

    P (2def) = 0.05 x 0.05 = 0.0025 *wrong

    Alternative route > (5/100) x (4/99) = 0.00202 *wrong
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  2. #2
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    You're dealing with binomial distribution  X \sim {\cal B}(n, p) where n=4, and p=0.05.

    So you have to find P(X=2) with P(X=k)=\left({n \atop k}\right) p^k(1-p)^{n-k}

    At least one defective case can be found using probability of the complement
    P(X\geq 1)=1-P(X=0).
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  3. #3
    Junior Member BobBali's Avatar
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    Thanks MathoMan.. You are right.

    I looked up Binomial Probability Distribution Function and it does correspond to what you have shown above.

    Regards,

    Bob
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