A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection (Diaconis and Mosteller 1989). Given a large number of events, extremely unlikely coincidences are possible--and perhaps even common. To quote Sherlock Holmes from "The Adventure of the Blue Carbuncle," "Amid the action and reaction of so dense a swarm of humanity, every possible combination of events may be expected to take place, and many a little problem will be presented which may be striking and bizarre..." (Conan Doyle 1892, p. 245).
See alsoBirthday Problem, Law of Truly Large Numbers, Odds, Principle of Insufficient Reason, Probability, Random, Significance
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ReferencesBogomolny, A. "Coincidence." http://www.cut-the-knot.org/do_you_know/coincidence.shtml.Conan Doyle, A. "The Adventure of the Blue Carbuncle." The Strand 3, 73-85, Jan. 1892. Reprinted in The Complete Sherlock Holmes. New York: Doubleday, pp. 244-257, 1988.Falk, R. "On Coincidences." Skeptical Inquirer 6, 18-31, 1981-82.Falk, R. "The Judgment of Coincidences: Mine Versus Yours." Amer. J. Psych. 102, 477-493, 1989.Falk, R. and MacGregor, D. "The Surprisingness of Coincidences." In Analysing and Aiding Decision Processes (Ed. P. Humphreys, O. Svenson, and A. Vári). New York: Elsevier, pp. 489-502, 1984.Diaconis, P. and Mosteller, F. "Methods of Studying Coincidences." J. Amer. Statist. Assoc. 84, 853-861, 1989.Jung, C. G. Synchronicity: An Acausal Connecting Principle. Princeton, NJ: Princeton University Press, 1973.Kammerer, P. Das Gesetz der Serie: Eine Lehre von den Wiederholungen im Lebens--und im Weltgeschehen. Stuttgart, Germany: Deutsche Verlags-Anstahlt, 1919.Peterson, I. "MathTrek: Birthday Surprises." Nov. 23, 1998. http://www.sciencenews.org/19981123/mathtrek.asp.Stewart, I. "What a Coincidence!" Sci. Amer. 278, 95-96, June 1998.
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Weisstein, Eric W. "Coincidence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Coincidence.html