Definition:Disjoint Events

Definition

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.

Sources

• Geoffrey Grimmett: Probability: An Introduction (1986): $\S 1.3$