"OR" Event

Definition

An 'OR' event in probability occurs when at least one of multiple events happens. The probability of an 'OR' event is calculated by adding the probabilities of individual events and subtracting the probability of their intersection.

5 Must Know Facts For Your Next Test

1. The formula for calculating the probability of an 'OR' event is $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
2. If two events are mutually exclusive, the formula simplifies to $P(A \cup B) = P(A) + P(B)$ because $P(A \cap B) = 0$.
3. Mutually exclusive events cannot happen at the same time.
4. 'OR' events are also known as the union of events in set theory notation.
5. Understanding 'OR' events is crucial for solving problems involving combined probabilities.

Review Questions

• What is the formula for calculating the probability of an 'OR' event?
• How does the formula for an 'OR' event change if two events are mutually exclusive?
• Explain why we subtract $P(A \cap B)$ when calculating $P(A \cup B)$.

Related terms

Mutually Exclusive Events:

Events that cannot occur simultaneously. If one event happens, the other cannot.

Intersection:

$A \cap B$ represents the occurrence of both A and B happening at the same time.

Union:

$A \cup B$ represents either event A happening, or event B happening, or both occurring.