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Math Help - Probability Question

  1. #1
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    Probability Question

    Suppose that 100 people enter a contest and that different winners are selected at random for first, second and third prizes. What is the probability that kumar, janice and pedro each win a prize if each entered the contest?

    Is this correct? 1/100 + 1/99 + 1/98?
    Thanks for your help.
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  2. #2
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    Hello, vexiked!

    Suppose that 100 people enter a contest and that different winners
    are selected at random for first, second and third prizes.
    What is the probability that Kumar, Janice and Pedro each win a prize?

    Is this correct? . \frac{1}{100} + \frac{1}{99} +\frac{1}{98} ? . . . . no

    The probability that Kumar wins a prize is: . \frac{3}{100}

    And the prob. that Janice wins a prize is: . \frac{2}{99}

    Then the prob. that Pedro wins a prize is: . \frac{1}{98}


    The probability that all win a prize is: . \frac{3}{100}\cdot\frac{2}{99}\cdot\frac{1}{98} \;=\;\frac{1}{161,\!700}

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  3. #3
    MHF Contributor matheagle's Avatar
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    Correct.
    You can look at it as two groups of people, those three and the other 97.
    It's a hypergeometric with (3 choose 3) times (97 choose 0) divided by (100 choose 3).
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