Union of two events

Definition

The union of two events, denoted as $A \cup B$, is the event that occurs if at least one of the events $A$ or $B$ happens. It represents all outcomes that are in either event or both.

5 Must Know Facts For Your Next Test

1. The formula for the probability of the union of two events is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
2. If $A$ and $B$ are mutually exclusive, then $P(A \cup B) = P(A) + P(B)$ because $P(A \cap B) = 0$.
3. The union operation is commutative, meaning $A \cup B = B \cup A$.
4. The union operation is associative, meaning $(A \cup B) \cup C = A \cup (B \cup C)$.
5. Visual representation using Venn diagrams can help in understanding the concept of the union of two events.

Review Questions

• What is the probability formula for the union of two events?
• How does the probability formula for the union change if events are mutually exclusive?
• Can you explain why $(A \cup B) \cup C = A \cup (B \cup C)$ holds true?

Related terms

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

Mutually Exclusive Events: Two events are mutually exclusive if they cannot occur at the same time, meaning their intersection is empty: $P(A \cap B) = 0$.

$P(A | B)$: $P(A | B)$ denotes the conditional probability that event $A$ occurs given that event $B$ has occurred.