1. ## 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?

2. ## 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

3. ## 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?

4. ## Re: Probability proof

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