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Math Help - [SOLVED] Probability(defective)

  1. #1
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    [SOLVED] Probability(defective)

    Question:
    A computer accessories distributor obtains its supply of diskettes from manufacturers A and B, with 60% of the diskettes from manufacture A. The diskettes are packed by the manufacturers in packets of tens. The probability that a diskette produced by manufacturer A is defective is 0.05 whereas the probability that a diskette produced by manufacturer B is defective is 0.02.
    Find the probability that a randomly chosen packet contains exactly one defective diskette.
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  2. #2
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    Quote Originally Posted by stpmmaths View Post
    Question:
    A computer accessories distributor obtains its supply of diskettes from manufacturers A and B, with 60% of the diskettes from manufacture A. The diskettes are packed by the manufacturers in packets of tens. The probability that a diskette produced by manufacturer A is defective is 0.05 whereas the probability that a diskette produced by manufacturer B is defective is 0.02. Find the probability that a randomly chosen packet contains exactly one defective diskette.
    What a dated problem. One mass storage ‘stick’ stores more the ten packages of disks.
    Let D denote that the random chosen pack has exactly one defective disk.
    P(D) = P\left( {D \cap A} \right) + P\left( {D \cap B} \right) = P\left( {D|A} \right)P(A) + P\left( {D|B} \right)P(B).
    Now P\left( {D|A} \right)P(A)=\binom{10}{1}(0.05)(0.95)^9(0.6)

    Can you finsh?
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  3. #3
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    Yes, thanks.
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