Union of two events Definition - College Algebra Key Term

Definition

The union of two events in probability is the event that either one or both of the events occur. It is denoted as $A \cup B$.

The probability of the union of two events A and B is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
The formula accounts for double-counting the probability where both events occur, which is why $P(A \cap B)$ is subtracted.
If A and B are mutually exclusive events, then $P(A \cup B) = P(A) + P(B)$ since $P(A \cap B) = 0$.
The concept of unions can be extended to more than two events using similar principles.
Understanding unions is crucial for solving complex probability problems involving multiple events.

Intersection of Two Events: The intersection of two events A and B, denoted as $A \cap B$, is the event that both A and B occur.

Events that cannot happen at the same time. For such events, $P(A \cap B) = 0$.

$\sigma$-algebra: A collection of sets closed under complementation and countable unions, used in advanced probability theory.