# 4.3 Independence & Causality

## Independent vs. Disjoint

Can two events be both disjoint and independent?

Exercise 1

Events $$A$$ and $$B$$ are disjoint if $$A\cap B=\emptyset$$ and they are independent if $$\Pr[A\cap B]=\Pr[A]\Pr[B]$$. If $$A\cap B=\emptyset$$, then since $$\Pr[\emptyset]=0$$, we need either $$\Pr[A]=0$$ or $$\Pr[B]=0$$ for them to be independent as well.