
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(AB)>=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?

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(ab)=.5=p(a) and So B favors A.
p(ca) = 1/6 = p(c) so A favors C
p(cb) = 0 and p(c)=1/6 and thus p(cb)< p(c) and so we have B favors A, A favors C and C doesn't favor B

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?

Re: Probability proof
yep... after I also failed trying to prove it =)