

A091715


Numerator Q of probability P=Q(n)/365^(n1) that three or more out of n people share the same birthday.


2



1, 1457, 1326781, 966556865, 616113172585, 359063094171965, 196176047915944825, 102076077386001384485, 51120278427593115164425, 24824896058243745467563925, 11753675337747799989826426225
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OFFSET

3,2


COMMENTS

A 365 day year and a uniform distribution of birthdays throughout the year is assumed. The probability that 3 or more out of n people share a birthday equals the probability A091674(n)/365^(n1) that 2 or more share a birthday minus the probability A091673(n)/365^(n1) that exactly 2 share a birthday.


LINKS

Table of n, a(n) for n=3..13.
Patrice Le Conte, Coincident Birthdays.
The Math Forum (AT) Drexel, Three Share a Birthday. Ask Dr. Math
Eric Weisstein's World of Mathematics, Birthday Problem. Section in World of Mathematics.


FORMULA

a(n)=A091674(n)A091673(n)


EXAMPLE

The probability that 3 or more people in a group of 10 share the same birthday is a(10)/365^9=102076077386001384485/114983567789585767578125~=8.87744913*10^4.
The probability exceeds 50% for n>A014088(3)=88.


CROSSREFS

Cf. A014088, A091673 Probabilities for exactly two, A091674 Probabilities for two or more.
Sequence in context: A235771 A235554 A255345 * A224528 A206147 A035764
Adjacent sequences: A091712 A091713 A091714 * A091716 A091717 A091718


KEYWORD

frac,nonn


AUTHOR

Hugo Pfoertner, Feb 04 2004


EXTENSIONS

Broken links corrected by Steven Finch, Jan 27 2009


STATUS

approved



