Union of two events

Definition

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

5 Must Know Facts For Your Next Test

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

Review Questions

• What is the formula for the probability of the union of two events?
• How does mutual exclusivity between two events affect their union's probability?
• Why do we subtract $P(A \cap B)$ when calculating $P(A \cup B)$?

Related terms

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.

Mutually Exclusive Events: 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.