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Math Help - Finding probabilities of two events.

  1. #1
    Junior Member
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    Finding probabilities of two events.

    Suppose 9 balls are distributed amongst 12 urns in such a way that no more than one ball is put in any one urn, and that all such arrangements are equally likely.

    (i) What is the probability that a specified urn will contain a ball?

    (ii) If the urns are placed in a row before the balls are distributed, what is the probability that at least two of the first four urns will be empty?



    Thanks for any help.
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  2. #2
    MHF Contributor
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    Sure this is a university level question?

    (i)
    You know 9 urns have a ball in, and there are 12 urns total. the probability you want is 9/12

    (ii)
    Work out

    P(at least 2 empty) = 1 - P(0 empty) - P(1 empty)

    P(0 empty)= \frac{9}{12} * \frac{8}{11} *  \frac{7}{10}* \frac{6}{9}

    P(1 empty) = \frac{9*8*7*3}{12*11*10*9} \times 4
    Last edited by SpringFan25; May 31st 2010 at 11:31 AM.
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