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Math Help - probability

  1. #1
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    Red face probability

    let 1<=r<=n. A subset of{1,2....n} of cardinality "r" is chosen at random. How do i calculate the probability that 1 is an element of the chosen subset
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    Quote Originally Posted by math8553 View Post
    let 1<=r<=n. A subset of{1,2....n} of cardinality "r" is chosen at random. How do i calculate the probability that 1 is an element of the chosen subset
    There are {{n-1} \choose {r-1}} subsets of \left\{ {1,2,3, \cdots ,n} \right\} that contain the element 1.
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    The number of subset of cardinality r is
    {{n} \choose {r}}
    and the number of those that doesn't contain 1 is {{n-1} \choose {r-1}} as Plato told you.
    The probability of taking a set that doesn't contain 1 is  {{n-1} \choose {r-1}}/{{n} \choose {r}}
    Last edited by vincisonfire; October 19th 2008 at 09:27 AM.
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