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Simple Approximation Formulas for the Birthday Problem

Matthias Arnold and andWerner Glaß
The American Mathematical Monthly
Vol. 120, No. 7 (August–September 2013), pp. 645-648
DOI: 10.4169/amer.math.monthly.120.07.645
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.07.645
Page Count: 4
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Simple Approximation Formulas for the Birthday Problem
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Abstract

Abstract We approximate the probability for at least k = 2 or 3 of n persons having the same birthday if we ignore leap years and assume that each day is equally likely. Although there are exact formulas available in the literature, a possible drawback to using them in the classroom is that these formulas are comparatively cumbersome. As an alternative, we suggest an easily computable approximation that still provides a close fit. Furthermore, the approximation allows an easy answer to the question of how many people are needed, so that the probability of at least two or three of them having the same birthday exceeds a given value.

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