Mutually exclusive events Definition - College Algebra Key Term

Definition

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

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

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

$P(A|B)$ 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.