---
tag: 0RWE7CPJ32
kind: concept
name: Probability theory
aliases: [probability-calculus]
msc: [60A05]
sources:
  - url: https://en.wikipedia.org/wiki/Probability_theory
    locator: lead section
same_as:
  wikidata: Q5862903
  wikipedia: Probability theory
---

## Summary

Probability theory is the branch of mathematics that studies chance in a precise way.
It models a random experiment by a [[probability space|0ZYBZ34RT2]]: a sample space, a family of events and a probability measure that obeys the [[probability axioms|0DAX8PMAJ4]].
Its main objects are events, random variables, their distributions and their expected values.
Its main results include limit theorems, such as the law of large numbers and the central limit theorem.

## Remarks

The modern axioms are due to Andrey Kolmogorov, who based them on measure theory in 1933.
Statistics uses probability theory to draw conclusions from data.

## Explanations

### L1 human

Probability theory gives numbers to uncertain things, such as the chance of rain or the chance of a six on a die.
The rules for these numbers are few and simple, but they give strong results.
For example, the average of many fair coin tosses is close to one half.