# Are disjoint events independent?

For disjoint $P \left(A \setminus \cap B\right) = 0$
For independence, $P \left(A \setminus \cap B\right) = P \left(A\right) \cdot P \left(B\right)$
If two disjoint events are independent then $P \left(A \setminus \cap B\right) = 0 = P \left(A\right) \cdot P \left(B\right)$
$\implies P \left(A\right) = 0$ or $P \left(B\right) = 0$