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%).
| Rule | Formula | US Term | UK / IB Term |
|---|---|---|---|
| Addition Rule | P(A∪B) = P(A)+P(B)−P(A∩B) | Union probability | Addition law |
| Multiplication Rule | P(A∩B) = P(A)×P(B) | Independent events | Multiplication law (independent) |
| Conditional | P(A|B) = P(A∩B)/P(B) | Conditional probability | Conditional probability |
| Complement Rule | P(A') = 1 − P(A) | Complement | Complement / P(A') |
| Bayes Theorem | P(A|B) = P(B|A)P(A)/P(B) | Bayesian inference | Bayes 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.