Thread: 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(B|A)<P(B). Is it true that P(A|B)<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(B|A)<P(A). Is it true that P(A|B)<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:

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