Table of Contents
What Is Or Probability?
The "or" probability (also called the union probability) measures the chance that at least one of two events will happen. In probability theory, this is written as P(A ∪ B) and uses the addition rule to avoid double-counting outcomes shared by both events.
Understanding or-probability is critical in risk assessment, quality control, insurance, and any decision-making that involves multiple uncertain outcomes. For example, an insurance company may want to know the probability that a policy holder experiences event A (car accident) or event B (home damage) in a given year.
Addition Rule Formula
When events A and B are mutually exclusive (they cannot happen at the same time), P(A and B) = 0, simplifying the formula to P(A or B) = P(A) + P(B).
Examples Table
| P(A) | P(B) | P(A and B) | P(A or B) |
|---|---|---|---|
| 0.3 | 0.4 | 0 (exclusive) | 0.7 |
| 0.5 | 0.5 | 0.25 | 0.75 |
| 0.6 | 0.3 | 0.1 | 0.8 |
| 0.2 | 0.8 | 0.16 | 0.84 |
Mutually Exclusive vs Non-Exclusive
Two events are mutually exclusive if they cannot occur simultaneously. Drawing a heart or a spade from a single card draw are mutually exclusive. Drawing a heart or a king are not mutually exclusive because the king of hearts satisfies both.
- Mutually exclusive: P(A or B) = P(A) + P(B)
- Not mutually exclusive: P(A or B) = P(A) + P(B) − P(A and B)
- Always verify whether events share outcomes before choosing a formula.
Frequently Asked Questions
Can P(A or B) exceed 1?
No. Probability values range from 0 to 1. If your calculation yields a value above 1, the input values are inconsistent (P(A and B) must be less than or equal to both P(A) and P(B)).
What if I have three events?
Use the inclusion-exclusion principle: P(A or B or C) = P(A)+P(B)+P(C) − P(AB) − P(AC) − P(BC) + P(ABC). This generalizes to any number of events.
How is "or" different from "and"?
"Or" asks for the probability that at least one event occurs. "And" asks for the probability both events occur simultaneously. P(A or B) is always greater than or equal to P(A and B).