Mutually Exclusive Events

Two events $A$ and $B$ are mutually exclusive (or disjoint) if they cannot occur at the same time.

Formally:

$$A\cap B=\varnothing$$

If events are mutually exclusive, the probability of their union satisfies:

$$P(A\cup B)=P(A)+P(B)$$

Example

For a single roll of a die:

• $A=2$
• $B=5$

Then $A\cap B=\varnothing$, so they are mutually exclusive.