Editing Probability theory (section)

==History of probability==
{{Main|History of probability}}

The modern mathematical theory of [[probability]] has its roots in attempts to analyze [[game of chance|games of chance]] by [[Gerolamo Cardano]] in the sixteenth century, and by [[Pierre de Fermat]] and [[Blaise Pascal]] in the seventeenth century (for example the "[[problem of points]]").<ref>{{Cite journal|last=LIGHTNER|first=JAMES E.|date=1991|title=A Brief Look at the History of Probability and Statistics|url=https://www.jstor.org/stable/27967334|journal=The Mathematics Teacher|volume=84|issue=8|pages=623–630|doi=10.5951/MT.84.8.0623|jstor=27967334|issn=0025-5769}}</ref> [[Christiaan Huygens]] published a book on the subject in 1657.<ref>{{cite book|last=Grinstead|first=Charles Miller |author2=James Laurie Snell|title=Introduction to Probability|pages=vii|chapter=Introduction}}</ref> In the 19th century, what is considered the [[classical definition of probability]] was completed by [[Pierre-Simon Laplace|Pierre Laplace]].<ref>{{cite journal|last=Daston|first=Lorraine J.|date=1980|title=Probabilistic Expectation and Rationality in Classical Probability Theory|url=https://dx.doi.org/10.1016/0315-0860%2880%2990025-7|journal= Historia Mathematica|volume=7|issue=3|pages=234–260|doi=10.1016/0315-0860(80)90025-7 }}</ref>

Initially, probability theory mainly considered {{em|discrete}} events, and its methods were mainly [[combinatorics|combinatorial]]. Eventually, [[mathematical analysis|analytical]] considerations compelled the incorporation of {{em|continuous}} variables into the theory.

This culminated in modern probability theory, on foundations laid by [[Andrey Nikolaevich Kolmogorov]]. Kolmogorov combined the notion of [[sample space]], introduced by [[Richard von Mises]], and [[measure theory]] and presented his [[Kolmogorov axioms|axiom system]] for probability theory in 1933. This became the mostly undisputed [[axiom system|axiomatic basis]] for modern probability theory; but, alternatives exist, such as the adoption of finite rather than countable additivity by [[Bruno de Finetti]].<ref>{{cite web|url=http://www.probabilityandfinance.com/articles/04.pdf |title="The origins and legacy of Kolmogorov's Grundbegriffe", by Glenn Shafer and Vladimir Vovk |access-date=2012-02-12}}</ref>