Testing for independence: probability

Q. If P(A) = 0.5, P(B) = 0.6 and P(A∩B)=0.3, test whether A and B are independent.

A. The test for independence is: if P(A|B) = P(A) then A and B are independent.

To run the test, we need to find P(A|B). We get this from P(A|B) = P(A∩B)/P(B).

Here that number is  0.3/0.6 = 0.5.

Now, is the correct? Does P(A|B) = P(A)? Yes because 0.5 = 0.5. So A and B are independent.