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...
For the record if the assumption of a uniform distribution of birth dates
throughout the year is made, and if the year is assumed to have an integer
number of days in it, then the following formula obtains:
p = 1 - d!/((d-n)!*d^n)
Here p is the probability of there being *at least* 1 birthday match in the
group, n is the cardinality of the group, and d is the number of days in the
year. If we set d = 365 and n = 50 we get that p = 0.97037.... If we try to
crudely account for the possibility of there being a group member with a
Feb. 29th birthday by just interpolating the above formula for a noninteger
value of d = 365.2425 (length of the Gregorian year) we get p = 0.97030.
...
David Bowman
dbowman@gtc.georgetown.ky.us