LaTeX
P(A^c)=1-P(A)Variables
- A: event
- Aᶜ: complement
How to use this formula
Finds the probability that an event does not occur.
Important notes
- The event and its complement partition the sample space.
Quick example
If P(A)=0.3, P(Aᶜ)=0.7.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The event and its complement partition the sample space.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
If P(A)=0.3, P(Aᶜ)=0.7.
Common mistakes
- Do not substitute sample and population quantities interchangeably in Probability Complement 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 Complement 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^c)=1-P(A). - 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 Complement Rule used for?
Finds the probability that an event does not occur.
Can I copy this formula as LaTeX?
Yes. Copy P(A^c)=1-P(A) 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.