LaTeX
P(A)=\sum_i P(A\mid B_i)P(B_i)Variables
- Bᵢ: mutually exclusive exhaustive events
How to use this formula
Combines conditional probabilities across a partition.
Important notes
- Every Bᵢ should have positive probability when conditioning.
Quick example
Useful before applying Bayes theorem.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Every Bᵢ should have positive probability when conditioning.
- For the Law of Total Probability, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
Useful before applying Bayes theorem.
Common mistakes
- Do not omit the index or bounds in Law of Total Probability; changing either one changes which terms are included.
- Do not assume events are independent or mutually exclusive unless the problem states or proves that condition.
Continue the workflow
Use Law of Total Probability 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)=\sum_i P(A\mid B_i)P(B_i). - 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 Law of Total Probability used for?
Combines conditional probabilities across a partition.
Can I copy this formula as LaTeX?
Yes. Copy P(A)=\sum_i P(A\mid B_i)P(B_i) 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.