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A091715 Numerator Q of probability P=Q(n)/365^(n-1) that three or more out of n people share the same birthday. 2
1, 1457, 1326781, 966556865, 616113172585, 359063094171965, 196176047915944825, 102076077386001384485, 51120278427593115164425, 24824896058243745467563925, 11753675337747799989826426225 (list; graph; refs; listen; history; text; internal format)
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^(n-1) that 2 or more share a birthday minus the probability A091673(n)/365^(n-1) 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

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Last modified August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)