LaTeX
P(A\cup B)=P(A)+P(B)-P(A\cap B)Variables
- A,B: events
How to use this formula
Finds the probability of at least one of two events.
Important notes
- For mutually exclusive events, the intersection term is zero.
Quick example
Use it to avoid double-counting overlap.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For mutually exclusive events, the intersection term is zero.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
Use it to avoid double-counting overlap.
Common mistakes
- Do not substitute sample and population quantities interchangeably in Probability Addition Rule; map every symbol to its definition first.
- Do not assume events are independent or mutually exclusive unless the problem states or proves that condition.
Continue the workflow
Use Probability Addition Rule in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
P(A\cup B)=P(A)+P(B)-P(A\cap B). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Probability Addition Rule used for?
Finds the probability of at least one of two events.
Can I copy this formula as LaTeX?
Yes. Copy P(A\cup B)=P(A)+P(B)-P(A\cap B) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.