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| The '''law of truly large numbers''', attributed to [[Persi Diaconis]] and [[Frederick Mosteller]], states that with a sample size large enough, any outrageous thing is likely to happen.<ref>{{Harvnb|Everitt|2002}}</ref> Because we never find it notable when likely events occur, we highlight unlikely events and notice them more. The law seeks to debunk one element of supposed supernatural [[Phenomenology (philosophy)|phenomenology]].
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| ==Example==
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| For a simplified example of the law, assume that a given event happens with a probability of 0.1% in one trial. Then the probability that this unlikely event does ''not'' happen in a single trial is 99.9% = 0.999.
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| In a sample of 1000 independent trials, the probability that the event does not happen in any of them is <math>0.999^{1000}</math>, or 36.8%. The probability that the event happens at least once in 1000 trials is then 1 − 0.368 = 0.632 or 63.2%. The probability that it happens at least once in 10,000 trials is <math>1 - 0.999^{10000} = 0.99995 = 99.995 %</math>.
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| This means that this "unlikely event" has a probability of 63.2% of happening if 1000 chances are given, or over 99.9% for 10,000 chances. In other words, a highly unlikely event, given enough tries, is even more likely to occur.
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| ==In pseudoscience==
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| The law comes up in [[pseudoscience]] and is sometimes called the [[Jeane Dixon effect]] (see also [[Postdiction]]). It holds that the more predictions a psychic makes, the better the odds that one of them will "hit". Thus, if one comes true, the psychic expects us to forget the vast majority that did not happen.
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| Humans can be susceptible to this fallacy. A similar manifestation can be found in [[gambling]], where gamblers tend to remember their wins and forget their losses and thus hold an inflated view of their real winnings.
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| [[Steven Novella]] describes this as the "lottery fallacy":
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| <blockquote>It is also the lottery fallacy. If we hold a world-wide lottery and only one human in the 6.5 billion wins, the odds of that person winning is very small. But someone had to win. Chopra and Lanza are arguing that the winner could not have one<!--the misspelling is in the original-->{{sic}} by chance alone, because the odds were against it.<ref>{{cite web |url=http://www.theness.com/neurologicablog/?p=1357 |title=Biocentrism Pseudoscience |publisher=NeuroLogica Blog |author=Steven Novella |authorlink=Steven Novella |accessdate=2010-05-17 }}</ref></blockquote>
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| ==See also==
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| *[[Coincidence]]
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| *[[Large numbers]]
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| *[[Law of large numbers]]
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| *[[Law of small numbers (disambiguation)|Law of small numbers]]
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| *[[Littlewood's law]]
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| *[[Miracle]]
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| *[[Psychic phenomena]]
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| *[[Infinite monkey theorem]]
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| * {{mathworld|LawofTrulyLargeNumbers}}
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| * {{cite journal
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| |last1=Diaconis |first1=P. |authorlink1=Persi Diaconis
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| |last2=Mosteller |first2=F. |authorlink2=Frederick Mosteller
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| |title=Methods of Studying Coincidences
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| |journal=Journal of the American Statistical Association
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| |volume=84 |issue=408 |pages=853–861 |year=1989
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| | mr = 1134485
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| |url=http://stat.stanford.edu/~cgates/PERSI/papers/mosteller89.pdf |accessdate=2009-04-28
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| |doi=10.2307/2290058
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| |publisher=American Statistical Association
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| |jstor=2290058
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| }}
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| *{{cite book |last= Everitt |first= B.S. |year= 2002 |title= Cambridge Dictionary of Statistics |edition= 2nd |isbn= 052181099X |ref= {{Harvid|Everitt|2002}}}}
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| ==External links==
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| * [http://skepdic.com/lawofnumbers.html skepdic.com on the ''Law of Truly Large Numbers'']
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| * [http://www.quackwatch.org/04ConsumerEducation/coincidence.html on the ''Law of Truly Large Numbers'']
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| [[Category:Probability theory]]
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| [[Category:Pseudoscience]]
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| [[Category:Statistical laws]]
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