If two events are mutually exclusive, their intersection is empty: $P(A \cap B) = 0$.
The probability of either of two mutually exclusive events occurring is the sum of their individual probabilities: $P(A \cup B) = P(A) + P(B)$.
Mutually exclusive events are also known as disjoint events.
In a Venn diagram, mutually exclusive events do not overlap.
If $A$ and $B$ are mutually exclusive, then $P(A \cup B \cup C)$ for another event $C$ can be calculated using: $P(A) + P(B) + P(C) - P(A \cap C) - P(B \cap C)$.
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?
Why can't mutually exclusive events have a non-zero intersection?
Related terms
Independent Events: Two events are independent if the occurrence of one does not affect the occurrence of the other: $P(A \cap B) = P(A)P(B)$.
Complementary Events: Two complementary events are those whose probabilities add up to one, representing all possible outcomes together: $P(A') = 1 - P(A)$.
Union of Events: $\text{The union of two or more events represents all outcomes that belong to at least one of these events: } P(A \cup B).$