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Math Help - probability question

  1. #1
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    probability question

    A parking lot contains 100 cars that all look quite nice from the outside.
    However, k of these cars happen to be lemons. The integer k is known to lie in the range
    {0,1,2,,9} with all values equally likely.
    (a) We testdrive 20 cars chosen at random without replacement, and to our pleasant surprise, none of them turn out to be a lemon. Given this knowledge, what is the probability that k = 0 .
    (b) Repeat part (a) when the 20 cars are chosen with replacement.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by inneedofhelp View Post
    A parking lot contains 100 cars that all look quite nice from the outside.
    However, k of these cars happen to be lemons. The integer k is known to lie in the range
    {0,1,2,…,9} with all values equally likely.
    (a) We testdrive 20 cars chosen at random without replacement, and to our pleasant surprise, none of them turn out to be a lemon. Given this knowledge, what is the probability that k = 0 .
    (b) Repeat part (a) when the 20 cars are chosen with replacement.
    Use Bayes theorem:

    P(k=0| 20 OK) p(20 OK) = P(20 OK|k=0)p(k=0),

    you have p(k=0)=1/10, p(20 OK|k=0)=1. So you just need to evaluate:

    p(20 OK)= sum[p(20 OK|k=r)p(k=r), r=0 to 9]

    RonL
    Last edited by CaptainBlack; September 30th 2007 at 10:17 PM.
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