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As a mathematical foundation for [[statistics]], probability theory is essential to many human activities that involve quantitative analysis of data.<ref>[http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm Inferring From Data]</ref> Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in [[statistical mechanics]] or [[sequential estimation]]. A great discovery of twentieth-century [[physics]] was the probabilistic nature of physical phenomena at atomic scales, described in [[quantum mechanics]]. <ref>{{cite encyclopedia |title=Quantum Logic and Probability Theory |encyclopedia=The Stanford Encyclopedia of Philosophy |date=10 August 2021|url= https://plato.stanford.edu/entries/qt-quantlog/ }}</ref>
==History of
{{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.
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