I am reading Wasserman's book and his class notes. In the notes, I found the following statement
If A, B are disjoint, both having positive probability, then A and B cannot be independent.
Now, if A and B are disjoint, $\mathbb{P}(A\cap B) = \mathbb{P}(\phi) =0$. So mathematically $\mathbb{P}(A)$ or $\mathbb{P}(B)$ cannot both be positive. But I am getting utterly confused when I am thinking abuot 2 events that are dependent and disjoint. Can someone please clarify the relation between independence and being disjoint of 2 events?