In Happy Birthday, the question was if there are N people in a room, what is the probability that there are at least two people in the room who share a birthday?

What if instead exactly two was required? If there are N people in a room, what is the probability that there are exactly two people in the room who share a birthday?

(Note: Assume leap year doesn't exist, and the birthdays are randomly distributed throughout the year.)

(In reply to re(2): thoughts by Bob Smith)

The formula

P = (365!/(366-n)!)*(n-1)/365^n

predicts a P = 0.03220711 for n = 19.  In 20,000 trials that would be expected to produce only about 644 successes give or take about 30 or so, but (see my comment) the simulation produced over 6,000 successes.

Posted by Charlie on 2006-06-09 17:03:43