The article “Leap Year Birthdays” in the Feb. 29 edition of The Rider News, pointing out that four students in the Rider family celebrate birthdays on Feb. 29, raises the question of whether this number is unusual.
In probability, there is the concept of expected value. In this case the expected value of the number of students whose birthdays occur on Feb. 29 is the product of the number of students sampled, times the probability that any given student has a birthday on that date.
If we assume that birthdays are evenly distributed throughout any four-year cycle, containing 365 x 4 + 1 =1,461 days, then the probability of having a birthday on Feb. 29 is 1 out of 1,461, or approximately 0.0006845. Since there are about 5,700 students attending Rider, the expected number of Leap Year Day birthdates would be 5,700 divided by 1,461, or about 3.901. (The expected value is not necessarily one of the values you could get. It may be interpreted as the average of the values you would get if you repeated the computation with many different samples of size 5,700, chosen from the population at large.)
By the way, the probability of having exactly four students out of 5,700 with birthdays on Feb. 29 is approximately .1952, while the probability for having five is approximately .1523, of having three is around .2001, of having two is .1531, and of having one is about .0788.
— Dr. Charles Schwartz
Chair, Department of Mathematics