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?