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Thread: Probability Scenario

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    Probability Scenario




    Hereís the scenario:

    A committee of 9 people is deciding which 5 people of 14 candidates should be hired for a job.
    In order to be hired, a candidate must receive 5 votes.
    Each of the 9 people on the committee has 5 votes to give (i.e., each of the 9 can each only vote for five people).

    While itís possible that more than five of the candidates could receive 5 votes (right?) it seems pretty improbable. Thatís my question: how probable/improbable is it that more than 5 of the 14 would receive
    5 votes?

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    Re: Probability Scenario

    hi,
    I am sure there is a nice and fancy way to calculate this, but in case you are interested in the actual numbers running a quick simulation wirh 100000 voting runs gives: 0 candidates with more then 5 votes - 37%, 1 candidate 45%, 2 candidates 16%, 3 candidates 2%, 4 candidates 0,1% , 5 candidates 0.001%.

    regards

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    Re: Probability Scenario

    Quote Originally Posted by rogojel View Post
    I am sure there is a nice and fancy way to calculate this. . .
    And that way may be in
    http://www.cengage.com/resource_uplo...2770_65932.pdf

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    Re: Probability Scenario

    Is there a solution to this concrete pb?

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    Re: Probability Scenario


    Quote Originally Posted by CORWU671 View Post
    Hereís the scenario:

    A committee of 9 people is deciding which 5 people of 14 candidates should be hired for a job.
    In order to be hired, a candidate must receive 5 votes.
    Each of the 9 people on the committee has 5 votes to give (i.e., each of the 9 can each only vote for five people).

    While itís possible that more than five of the candidates could receive 5 votes (right?) it seems pretty improbable. Thatís my question: how probable/improbable is it that more than 5 of the 14 would receive
    5 votes?
    Well, assuming random selections by the judges, you're right that the probability of 6 candidates getting 5 votes from each of 9 judges is small (about 0.0003). But so is the probability of 5 candidates getting 5 votes rather small (about 0.005). It strikes me that if all of the 14 candidates are judged to be on a par, and all well qualified, that the resulting random selections by the judges would lead to similar low probabilities ...and none of the qualified candidates would be selected.

    Seems to me the process is geared to work fairly well only when a small handfull of candidates stand head-and-shoulders above the rest.

    Art

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