Mutually exclusive

Definition

Mutually exclusive events are two or more events that cannot occur at the same time. If one event happens, the other cannot.

5 Must Know Facts For Your Next Test

1. If events A and B are mutually exclusive, $P(A \cap B) = 0$.
2. The probability of either event A or event B occurring is given by $P(A \cup B) = P(A) + P(B)$ for mutually exclusive events.
3. Mutually exclusive events have no outcomes in common.
4. Another term for mutually exclusive events is disjoint events.
5. For two mutually exclusive events, knowing that one has occurred provides complete information about the non-occurrence of the other.

Review Questions

• What does it mean for two events to be mutually exclusive?
• How do you calculate the probability of either of two mutually exclusive events occurring?
• Can two independent events be mutually exclusive? Explain why or why not.

Related terms

Independent Events: Two or more events are independent if the occurrence of one does not affect the probability of occurrence of the other(s).

$P(A \cup B)$: $P(A \cup B)$ represents the probability that either event A or event B occurs.

$P(A \cap B)$: $P(A \cap B)$ represents the probability that both event A and event B occur at the same time.