# Probability Question

1. Sep 24, 2008

### Dragonfall

1. The problem statement, all variables and given/known data
Given that $$P[A|B]=P[A|B^c]$$, prove that they are independent.

3. The attempt at a solution

So we have that $$\frac{P(A\cap B)}{P(B)}=\frac{P(A\cap B^c)}{P(B^c)}$$. I would have to show that $$\frac{P(A\cap B^c)}{P(B^c)}=P(A)$$. I can't make that happen.

2. Sep 24, 2008

### danago

Try using the fact that $$P(A \cap \overline B ) = P(A) - P(A \cap B)$$, i think.

3. Sep 24, 2008

### Dragonfall

Got it. This was unusually convoluted for something so trivial.