Easy conditional probability question

Question

I'm beginning to grasp on to conditional probability, but I have a quick and dirty question that I cannot find the answer to on the internet (but I think is really easy). Is P(B|A) equal to P(B)?

Thanks

Answer 1

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

$P(B|A)=P(B)$ if and only if $A$ and $B$ are independent. If they are then, $$P(B|A)=\frac{P(B\cap A)}{P(A)}=\frac{P(B)P(A)}{P(A)}=P(B).$$