Mutually exclusive events

Definition

Mutually exclusive events are 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 $A$ and $B$ are mutually exclusive, then $P(A \cup B) = P(A) + P(B)$.
2. The intersection of mutually exclusive events is always zero: $P(A \cap B) = 0$.
3. Mutually exclusive is different from independent; mutually exclusive events are dependent because the occurrence of one affects the probability of the other.
4. In a Venn diagram, mutually exclusive events do not overlap.
5. For any two events to be mutually exclusive, their combined probability cannot exceed 1.

Review Questions

• What is the probability of the intersection of two mutually exclusive events?
• How does mutual exclusivity affect the addition rule in probability?
• Can two independent events be mutually exclusive? Why or why not?

Related terms

Independent Events: Two events are independent if the occurrence of one does not affect the probability of the other.

Conditional Probability:

$P(A|B)$ is the probability of event $A$ occurring given that event $B$ has occurred.

Complementary Events: Two events are complementary if they are mutually exclusive and their probabilities sum to one.