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Math Help - Combinations/Probability

  1. #1
    Fel
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    Combinations/Probability

    A rental car service facility has 10 foreign cars and 15 domestic cars. Choose 6 cars at random. Let D_i={exactly i of 6 cars chosen are domestic}, i=0,1,2,...6. What is the probability of at least 3 cars out of the 6 being domestic? I'm not sure how to solve this. Any help is appreciated.
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  2. #2
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    Maybe

    A = 10 choose i
    B = 15 choose 6-i
    C = 25 choose i

    P(D_i) = AB / C

    What could be done is checking that the sum of D_i is one.
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  3. #3
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    Quote Originally Posted by Fel View Post
    A rental car service facility has 10 foreign cars and 15 domestic cars. Choose 6 cars at random. Let D_i={exactly i of 6 cars chosen are domestic}, i=0,1,2,...6. What is the probability of at least 3 cars out of the 6 being domestic? I'm not sure how to solve this. Any help is appreciated.
    D_k=\dbinom{15}{k}\dbinom{10}{6-k} .

    Consider \dfrac{{\sum\limits_{k = 3}^6 {D_k } }}<br />
{\binom{25}{6}}
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