OFFSET
3,2
COMMENTS
A 365-day year and a uniform distribution of birthdays throughout the year are 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
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.
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
KEYWORD
frac,nonn
AUTHOR
Hugo Pfoertner, Feb 04 2004
STATUS
approved