
Conditional Probability
I have been working on two problems and keep confusing myself. Any help would be appreciated.
Here they are....
1) Let A and B be events from a sample space, with P(A)>0 and P(B)>0 and such that P(BA)<P(B). Is it true that P(AB)<P(A)?
2) Let A and B be events from a sample space, with P(A)>0 and P(B)>0 and such that P(BA)<P(A). Is it true that P(AB)<P(B)?
I know that if it is false, i need to have a counter example, but i am completely stuck on this. I keep confusing myself.

Here's what I'm thinking:
$\displaystyle P(BA) = \frac{P(BA)}{P(A)} < P(B)$
$\displaystyle P(BA) < P(B)P(A)$
$\displaystyle \frac{P(BA)}{P(B)} < P(A)$
$\displaystyle P(AB) < P(A)
$

This works for this one, but for the second one it will not. Therefore a counterexample will be needed. so how would i go about finding a counterexample.