Question

Which statement implies that A and B are independent events?

Answer 1

The events $A,B$ are independent if and only if $P(A\cap B)=P(A)\cdot P(B)$. Under this condition, we have conditional probabilities

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)$

$P(B\mid A)=P(B)$

so the answer is D.