 
Summary: THE BIRTHDAY PROBLEM WITH
LEAP YEAR BIRTHDAYS TAKEN INTO ACCOUNT
MATH 5651, FALL 2011
PROF. GREG W. ANDERSON
Ignoring the problem of birthdays on February 29, as explained in class and in
our textbook by DeGroot and Schervish, we have
(1) Pr(k people in a room have distinct birthdays) =
P365,k
365k
.
These probabilities (actually the complementary probabilities) are tabulated in
Chap. 1 Sec. 7 of our textbook. It is (perhaps) surprising that k = 23 makes the
probability on line (1) very nearly equal to 1
2 . Sadly, the experiment I ran in class
to see if we had any overlapping birthdays failed. It seems that everybody in the
class has different birthdays! There is only a 0.1 chance of that happening in a
roomful of 40 people.
The question came up in class how to correct the book's calculations to account
for leap years. I could not answer in real time. But I thought it through as I was
walking home this evening and came up with the answer
