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Math Help - Please help

  1. #1
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    Please help

    "Of three urns, the first contains 2 white and 4 black cards, the second contains 8 white and four black cards, and 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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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    Use Poisson's rule.
    Let A_1: the card drawn from the first urn is white.
    A_2: the card drawn from the second urn is white.
    A_3: the card drawn from the third urn is white.
    We have:
    p_1=p(A_1)=\frac{1}{2}, \ q_1=\frac{1}{2}
    p_2=p(A_2)=\frac{2}{3}, \ q_2=\frac{1}{3}
    p_3=p(A_3)=\frac{1}{4}, \ q_3=\frac{3}{4}

    So, the probability that exactly two cards are white is equal to the coefficient of x^2 in the expression
    (p_1x+q_1)(p_2x+q_2)(p_3x+q_3)
    That means p_1p_2q_3+p_1q_2p_3+q_1p_2p_3.
    Now, plug in p_1,p_2,p_3,q_1,q_2,q_3.
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