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Math Help - Combinatorial probability question

  1. #1
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    Combinatorial probability question

    im sure this will be easy for most, i just am having trouble knowing where to start as im new to probability. the question is as follows:

    "A science committee of 3 people is to be formed from a group of 17 scientists (7 biologists, 4
    physicists and 6 chemists) with each possible committee equally likely.
    What is the probability the committee vote in favour of a proposal given:

    (a) all biologists in favour, everybody else against?
    (b) all chemists against, everybody else in favour?
    (c) all biologists in favour, all chemists against and all physicists abstain?"


    thanks
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  2. #2
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    In order to do this we must assume that a proposal passes on simple majority vote: 2 to 1 or 3 to 0.
    To do part (a) then we must have two biologists and one other or all three biologists.
    What is the probability of each of those committees?
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  3. #3
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    Quote Originally Posted by Plato View Post
    In order to do this we must assume that a proposal passes on simple majority vote: 2 to 1 or 3 to 0.
    To do part (a) then we must have two biologists and one other or all three biologists.
    What is the probability of each of those committees?
    7 choose 2 times by 10 choose 1??
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  4. #4
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    What about all three?
    \displaystyle\frac{\binom{7}{2}\binom{10}{1}}{\bin  om{17}{3}}+\frac{\binom{7}{3}\binom{10}{0}}{\binom  {17}{3}}.

    That answers part (a).
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