Definition:Disjoint Events

Let $$A$$ and $$B$$ be events in a probability space.

Then $$A$$ and $$B$$ are disjoint iff:
 * $$A \cap B = \varnothing$$

It follows by definition of probability measure that $$A$$ and $$B$$ are disjoint iff:
 * $$\Pr \left({A \cap B}\right) = 0$$

That is, two events are disjoint iff the probability of them both occurring in the same experiment is zero.

That is, iff $$A$$ and $$B$$ can't happen together.

$$A$$ and $$B$$ are also referred to in this context as mutually exclusive.