Mutual Exclusivity

3. Probability: Relationship between Events

Mutual Exclusivity

In some cases, two events will have overlapping outcomes.
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The event of rolling a die and getting an even number $\{2, 4, 6\}$ has overlapping outcomes with the event of rolling a die and getting a number greater than 2 $\{3, 4, 5, 6\}$ ; namely the outcomes $4$ and $6$ .

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Other events do not overlap at all. Such events are said to be mutually exclusive.
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The event of rolling an odd number $\{1, 3, 5\}$ and the event of rolling an even number $\{2, 4, 6\}$ have no overlapping outcomes at all.

Mutual exclusivity

Definition

Two events $A$ and $B$ are mutually exclusive or disjoint when they have no outcomes in common.

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Note that any event $A$ and its complement $A^c$ are, by definition, mutually exclusive.