Classroom Birthdays


Only 23 students. In fact, if the class held 40 students, the liklihood of a common birthday is 90%, a near certainty.

Let's calculate the probability that, in a class of N students, no one has the same birthday date (we'll ignore leap years). The N students are placed in a line, with the first student free to have any birth date. The second student must avoid that date, being restricted to 364 days of the year. The third person is restricted to any of 363 dates... with the Nth student restricted to 366 - N dates. The probability, Q, of there being no common birthday is thus

Q = (364 / 365)(363 / 365)(362 /365)....((366 - N) / 365)

The probability that there is at least one common birthday is thus P = 1 - Q. P is presented as a function of the number of class students in the displayed figure below.