What is the quantitative method to check statistically independent events?
A and B are independent events if one of the following three conditions are satisfied:
1. $\displaystyle \Pr(A \cap B) = \Pr(A) \cdot \Pr(B)$
2. $\displaystyle \Pr(A | B) = \Pr(A)$.
3. $\displaystyle \Pr(B | A) = \Pr(B)$.
So pick one of these conditions and check whether or not it holds.