🇺🇸 AP Statistics 🇬🇧 A-Level Maths 🌐 IB Mathematics 🎓 Frequentist / Bayesian

Probability Calculator

Calculate combined probabilities: union (A or B), intersection (A and B), conditional (A given B), and complement (not A). Enter probabilities as decimals (0.4 = 40%).

Quick Reference
P(A∪B) = P(A) + P(B) − P(A∩B)  ·  P(A∩B) = P(A)×P(B) [independent]  ·  P(A|B) = P(A∩B)/P(B)  ·  P(A') = 1 − P(A)
Rule Formula US Term UK / IB Term
Addition Rule P(A∪B) = P(A)+P(B)−P(A∩B)Union probabilityAddition law
Multiplication Rule P(A∩B) = P(A)×P(B)Independent eventsMultiplication law (independent)
Conditional P(A|B) = P(A∩B)/P(B)Conditional probabilityConditional probability
Complement Rule P(A') = 1 − P(A)ComplementComplement / P(A')
Bayes Theorem P(A|B) = P(B|A)P(A)/P(B)Bayesian inferenceBayes theorem (HL topic)

Frequently Asked Questions

What is the difference between frequentist and Bayesian probability?

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.

How do probability curricula differ globally?

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.