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(4): thoughts by Bob Smith)

Kudos to Robby for seeing the way forward.

Adding a factor of n/2 to my formula brings it in agreement with Charlie's.

 

Posted by Bob Smith on 2006-06-12 09:12:34