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Math Help - Probability proof

  1. #1
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    Oct 2011
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    Probability proof

    Hi just started probability and not sure if I'm on the the right track with this question. It gives that event B favours event A if P(A|B)>=P(A).

    It then asks to prove the following statement or give counterexample; "if B favours A, and A favours C then B favours C"

    I have tried proving it but cannot find how to link events B and C through event A despite numerous attempts. I tried suggesting they are independent events but then they are all just individually equal so it holds. Its possible it isn't true but I can't think of a counterexample that proves it wrong.

    Any ideas on what Im doing wrong?
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  2. #2
    Junior Member
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    Re: Probability proof

    This is not a true statement.

    A:flipping a heads (on a fair coin)
    B:rolling an even number (on a 6 sided normal die)
    C:rolling a 5 (on a 6 sides normal die)

    P(a|b)=.5=p(a) and So B favors A.

    p(c|a) = 1/6 = p(c) so A favors C

    p(c|b) = 0 and p(c)=1/6 and thus p(c|b)< p(c) and so we have B favors A, A favors C and C doesn't favor B
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  3. #3
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    Re: Probability proof

    Thanks thats a good example, I'm guessing you looked for events B and C that were related and then picked an event A that was independent?
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  4. #4
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    Re: Probability proof

    yep... after I also failed trying to prove it =)
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