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Math Help - A tough one

  1. #1
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    A tough one

    There are three urns.
    1. The first contains 2 white and 4 black cards
    2. The second contains 8 white and four black cards
    3. The third contains 1 white and 3 black card.

    If one card is selected from each urn, find the probability that exactly 2 white cards are drawn"
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  3. #3
    Eater of Worlds
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    What Plato is getting at is suppose the two white cards come from urns 1 and 2, repectively. Therefore, the third card, black, must come from urn 3.
    So, (2/6)(8/12)(3/4)=1/6

    Now, do the same for the other two cases and add them up. Supoose they come from urns 1 and 3 and urns 2 and 3
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    case 1 (urn 1 and 2)
    (2/6)(8/12)(3/4) = 1/6

    Case 2 (Urn 2 and 3)
    (4/6)(8/12)(1/4) = 1/9

    Case 3 (Urn 1 and 3)
    (2/6)(4/12)(1/4) = 1/36

    Add them up

    1/6 + 1/9 + 1/36 = 0.305
    Last edited by Infiniti; October 22nd 2007 at 05:03 PM.
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  5. #5
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    Quote Originally Posted by Infiniti View Post
    case 1 (urn 1 and 2)
    (2/6)(8/12)(3/4) = 1/6

    Case 2 (Urn 2 and 3)
    (4/6)(8/12)(1/4) = 1/9

    Case 3 (Urn 1 and 3)
    (2/6)(4/12)(1/4) = 1/36

    Add them up

    1/6 + 1/9 + 1/36 = 0.305
    Since you have the fractions, why not add them and put the answer in terms of a fraction?
    \frac{1}{6} + \frac{1}{9} + \frac{1}{36}

    = \frac{6}{36} + \frac{4}{36} + \frac{1}{36}

    = \frac{11}{36}

    The value of doing this is that this is the exact answer, not an approximation.

    -Dan
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Infiniti View Post
    case 1 (urn 1 and 2)
    (2/6)(8/12)(3/4) = 1/6

    Case 2 (Urn 2 and 3)
    (4/6)(8/12)(1/4) = 1/9

    Case 3 (Urn 1 and 3)
    (2/6)(4/12)(1/4) = 1/36

    Add them up

    1/6 + 1/9 + 1/36 = 0.305
    Since Infiniti and Reward appear to be one and the same person, why are
    you answering your own question?

    RonL
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