# Conditional Probability

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• September 24th 2009, 05:35 PM
dude15129
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.
• September 24th 2009, 06:22 PM
jfz23
Here's what I'm thinking:

$P(B|A) = \frac{P(BA)}{P(A)} < P(B)$

$P(BA) < P(B)P(A)$

$\frac{P(BA)}{P(B)} < P(A)$

$P(A|B) < P(A)
$
• September 24th 2009, 06:36 PM
dude15129
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.