I have this question:
P(A | B)P(B) = P(B | A)P(A) if A and B are independent events.
My reasoning: If A & B are independent, P(A|B) = P(A) and P(B|A) = P(B) and the above expression reduces to P(A)*P(B) = P(B)*P(A), which proves that the statement is true.
However the answer indicates that it is not true. Any mistakes in my argument?
Thanks.