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Math Help - Probability-Bayes Theorem

  1. #1
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    Probability-Bayes Theorem

    Problem:

    The Belgian 20-Frank coin (B20), the Italian 500-Lire coin (L500), and the Hong Kong 5-Dollar (HK5) are approximately the same size. Coin purse one (C1) contains six of each of these coins. Coin purse two (C2) contains nine B20s, six I500s, and three HK5s. A fair four-sided die is rolled. If the outcome is {1}, a coin is selected randomly from C1. If the outcomes belong to {2, 3, 4}, a coin is selected randomly from C2.
    a) Find P(HK5).

    b) Find P(C2|HK5).

    I've drawn a tree diagram.
    Now for a), is this correct?  (3/4)(1/6)+(1/4)(1/3)=5/24

    And for b), do I use Bayes Theorem? Is this correct?  ((3/4)(1/6))/((3/4)(1/6)+(1/4)(1/3))=3/5

    Thanks for the help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by eri123 View Post
    Problem:

    The Belgian 20-Frank coin (B20), the Italian 500-Lire coin (L500), and the Hong Kong 5-Dollar (HK5) are approximately the same size. Coin purse one (C1) contains six of each of these coins. Coin purse two (C2) contains nine B20s, six I500s, and three HK5s. A fair four-sided die is rolled. If the outcome is {1}, a coin is selected randomly from C1. If the outcomes belong to {2, 3, 4}, a coin is selected randomly from C2.
    a) Find P(HK5).

    b) Find P(C2|HK5).

    I've drawn a tree diagram.
    Now for a), is this correct?  (3/4)(1/6)+(1/4)(1/3)=5/24
    Yes.

    And for b), do I use Bayes Theorem? Is this correct?  ((3/4)(1/6))/((3/4)(1/6)+(1/4)(1/3))=3/5
    You could use Bayes' theorem, but if you have a tree diagram I would just read the required sum off of that, but anyway your answer is correct.

    CB
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