We use the known equality: .
We also know that and use that on last fraction:
If [A|B] = [A|B complement], show that A and B are independent.
Here's what I've got so far:
Using the definition of conditional probability and the multiplicative law, I arrived at this:
P[A|B] = (P[B complement|A]*P[A])/P[B complement]
I'm not sure how I'm supposed to arrive at the definition of independence (P[A|B] = P[A]) from this.