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Math Help - Probability question above my pay grade.

  1. #1
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    Probability question above my pay grade.

    Greetings all.

    I have a small problem that I can't solve without doing it long hand and if possible I'd like to have a formula to solve it. Or the answer would be nice too.

    Setup:

    I have 6 people, 3 of which are bad guys and 3 are good guys. If I have to choose one out of the group as a bad guy then my odds are 50/50

    Take the same 6 people with the same spread... but limit my choice to only one of 4 random people.

    What are the odds of my 4 choices including all 3 bad guys

    What are the odds of my 4 choices including only 2 bad guys

    What are the odd of my 4 choices including only 1 bad guy.

    TIA

    SloMo

    Let me ask the question differently.

    Given the same two options as above... choose one of the entire 6 ... or choose one of a random 4.. What is the best decision based on probability.
    Last edited by mr fantastic; September 28th 2011 at 06:40 PM. Reason: Merged posts.
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  2. #2
    MHF Contributor
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    Re: Probability question above my pay grade.

    If you had a really large population, this would be a nice binomial problem. As it is, you may just going to have to count them. I'd start with a tree diagram.

    Of course, you could just calculate it.

    Just one of 4: \frac{{3 \choose 1}\cdot {3 \choose 3}}{{6 \choose 4}}

    You do 2 of 4.
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