Editing Probability axioms (section)

{{Short description|Foundations of probability theory}}
{{Probability fundamentals}}
The standard '''probability axioms''' are the foundations of [[probability theory]] introduced by Russian mathematician [[Andrey Kolmogorov]] in 1933.<ref name=":0">{{Cite book |title=Foundations of the theory of probability |url=https://archive.org/details/foundationsofthe00kolm |last=Kolmogorov |first=Andrey |publisher=Chelsea Publishing Company |year=1950 |orig-date=1933 |location=New York, US }}</ref> These [[axiom]]s remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases.<ref>{{Cite web |url=https://www.stat.berkeley.edu/~aldous/Real_World/kolmogorov.html |title=What is the significance of the Kolmogorov axioms? |last=Aldous |first=David |website=David Aldous |access-date=November 19, 2019}}</ref>

There are several other (equivalent) approaches to formalising probability. [[Bayesian theory|Bayesians]] will often motivate the Kolmogorov axioms by invoking [[Cox's theorem]] or the [[Dutch book argument|Dutch book arguments]] instead.<ref>{{Cite journal | last = Cox | first = R. T. | author-link = Richard Threlkeld Cox| doi = 10.1119/1.1990764 | title = Probability, Frequency and Reasonable Expectation | journal = American Journal of Physics | volume = 14 | pages = 1–10 | year = 1946 | issue = 1 | bibcode = 1946AmJPh..14....1C }}</ref><ref>{{cite book|first=R. T. |last=Cox |author-link=Richard Threlkeld Cox |title=The Algebra of Probable Inference |publisher=Johns Hopkins University Press |location=Baltimore, MD |year=1961 }}</ref>