---
title: "Probability Calculator — Union, Intersection, Conditional, Complement"
description: "Calculate P(A∪B), P(A∩B), P(A|B), and P(A'). Covers frequentist probability rules taught in AP Statistics (US), A-Level (UK), and IB Mathematics worldwide."
url: "https://worldcalculators.org/calculators/probability/"
canonical: "https://worldcalculators.org/calculators/probability/"
---

# Probability Calculator

Calculate P(A∪B), P(A∩B), P(A|B), and P(A'). Covers frequentist probability rules taught in AP Statistics (US), A-Level (UK), and IB Mathematics worldwide.

## Quick answer

Frequentist probability (taught in AP Stats, A-Level, IB) defines probability as the long-run frequency of an event in repeated trials. Bayesian probability treats probability as a degree of belief, updated with new evidence using Bayes' Theorem. Bayesian methods are standard in modern machine learning and medical diagnosis. UK A-Level introduces Bayes' theorem at A2 level; IB Math HL covers it; AP Statistics focuses on frequentist methods.

## Frequently Asked Questions

Frequentist probability (taught in AP Stats, A-Level, IB) defines probability as the long-run frequency of an event in repeated trials. Bayesian probability treats probability as a degree of belief, updated with new evidence using Bayes' Theorem. Bayesian methods are standard in modern machine learning and medical diagnosis. UK A-Level introduces Bayes' theorem at A2 level; IB Math HL covers it; AP Statistics focuses on frequentist methods.
US AP Statistics: covers all basic rules, conditional probability, binomial and geometric distributions, simulation. UK A-Level Statistics (S1/S2): similar coverage with emphasis on probability trees and Venn diagrams. IB Math AA HL: covers conditional probability and Bayes' theorem as mandatory content. IB Math AI SL: lighter treatment, more focus on data. Germany Abitur: probability covered in both Stochastik units; Bayesian methods increasingly included. Japan (数学B): combinatorics and probability including conditional probability, geometric probability.

Source: https://worldcalculators.org/calculators/probability/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.