THE BIRTHDAY PROBLEM WITH LEAP YEAR BIRTHDAYS TAKEN INTO ACCOUNT 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 Collections: Mathematics