User:Boris Tsirelson/Sandbox1

In this article leap years and other details are ignored.

To show how to calculate the probability of a group including such a match, it is simpler to first find the probability of all the birthdays being different. Consider a group of two people. The first person can have been born on any of the 365 days of the year, while the second must have been born on one of the other 364 days in order to not match. The first person has a probability of ${\tfrac {365}{365}}$ , which equals 1.0, and the second has a probability of ${\tfrac {364}{365}}$ which is 0.9973. Multiplying these probabilities together gives a net probability of 0.9973 for having different birthdays. Subtracting this number from 1.0 gives a 0.0027 probability of having the same birthday.

I have always felt that, if one day someone came up with a contradiction in mathematics, I would just say, "Well, those crazy logicians are at it again," and go about my business as I was going the day before.

References

Feynman, Richard (1995), The character of physical law (twenty second printing ed.), the MIT press, ISBN 0 262 56003 8.

Gowers, Timothy, ed. (2008), The Princeton companion to mathematics, Princeton University Press, ISBN 978-0-691-11880-2.

Mathias, Adrian (2002), "A term of length 4,523,659,424,929", Synthese 133 (1/2): 75–86. (Also here.)

Casacuberta, C & M Castellet, eds. (1992), Mathematical research today and tomorrow: Viewpoints of seven Fields medalists, Lecture Notes in Mathematics, vol. 1525, Springer-Verlag, ISBN 3-540-56011-4.