Editing Probability (section)

==Applications==
Probability theory is applied in everyday life in [[risk]] assessment and [[Statistical model|modeling]]. The insurance industry and [[Market (economics)|markets]] use [[actuarial science]] to determine pricing and make trading decisions. Governments apply probabilistic methods in [[environmental regulation]], entitlement analysis, and [[financial regulation]].

An example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. An assessment by a commodity trader that a war is more likely can send that commodity's prices up or down, and signals other traders of that opinion. Accordingly, the probabilities are neither assessed independently nor necessarily rationally. The theory of [[behavioral finance]] emerged to describe the effect of such [[groupthink]] on pricing, on policy, and on peace and conflict.<ref>Singh, Laurie (2010) "Whither Efficient Markets? Efficient Market Theory and Behavioral Finance". The Finance Professionals' Post, 2010.</ref>

In addition to financial assessment, probability can be used to analyze trends in biology (e.g., disease spread) as well as ecology (e.g., biological [[Punnett squares]]).<ref name="Edwards_2012_2">{{cite journal |title=Reginald Crundall Punnett: First Arthur Balfour Professor of Genetics, Cambridge, 1912 |author-first=Anthony William Fairbank |author-last=Edwards |author-link=Anthony William Fairbank Edwards |location=Gonville and Caius College, Cambridge, UK |date=September 2012 |journal=[[Genetics (journal)|Genetics]] |department=Perspectives |publisher=[[Genetics Society of America]] |volume=192 |issue=1 |pages=3–13 |doi=10.1534/genetics.112.143552 |pmc=3430543 |pmid=22964834 |quote-pages=5–6 |quote=[…] Punnett's square seems to have been a development of 1905, too late for the first edition of his ''Mendelism'' (May 1905) but much in evidence in ''Report III to the Evolution Committee of the Royal Society'' [(Bateson et al. 1906b) "received March 16, 1906"]. The earliest mention is contained in a letter to Bateson from Francis Galton dated October 1, 1905 (Edwards 2012). We have the testimony of Bateson (1909, p. 57) that "For the introduction of this system [the 'graphic method'], which greatly simplifies difficult cases, I am indebted to Mr. Punnett." […] The first published diagrams appeared in 1906. […] when Punnett published the second edition of his ''Mendelism'', he used a slightly different format ([…] Punnett 1907, p. 45) […] In the third edition (Punnett 1911, p. 34) he reverted to the arrangement […] with a description of the construction of what he called the "chessboard" method (although in truth it is more like a multiplication table). […]}} (11 pages)</ref> As with finance, risk assessment can be used as a statistical tool to calculate the likelihood of undesirable events occurring, and can assist with implementing protocols to avoid encountering such circumstances. Probability is used to design [[games of chance]] so that casinos can make a guaranteed profit, yet provide payouts to players that are frequent enough to encourage continued play.<ref>{{cite journal|last1=Gao|first1=J.Z.|last2=Fong|first2=D.|last3=Liu|first3=X.|title=Mathematical analyses of casino rebate systems for VIP gambling|journal=International Gambling Studies|date=April 2011|volume=11|issue=1|pages=93–106|doi=10.1080/14459795.2011.552575|s2cid=144540412}}<!--|access-date=13 October 2015--></ref>

Another significant application of probability theory in everyday life is [[reliability (statistics)|reliability]]. Many consumer products, such as [[automobiles]] and consumer electronics, use reliability theory in product design to reduce the probability of failure. Failure probability may influence a manufacturer's decisions on a product's [[warranty]].<ref>{{Cite journal | doi=10.1287/mnsc.1090.1132| title=Management Insights| journal=Management Science| volume=56| pages=iv–vii| year=2010| last1=Gorman| first1=Michael F.| doi-access=}}</ref>

The [[cache language model]] and other [[Statistical Language Model|statistical language models]] that are used in [[natural language processing]] are also examples of applications of probability theory.