Let’s make a couple of assumptions. First, let’s assume that birthdays are randomly distributed — given enough people, you’ll have roughly the same number born on say, December 13th as you will on November 22nd or April 14th. (As it turns out, this isn’t true.) Second, let’s assume that February 29th — Leap Day — doesn’t exist. (Also untrue.) And, finally, let’s assume that everyone uses the 365-day Gregorian calendar. (Mostly true.) Got it? Nothing too controversial. Say you walk into an empty auditorium. A minute or so later, someone else walks in. Again making the assumptions above, there’s a 1 in 365 chance (0.27%) that this person shares your birthday. A second person walks in a minute or two later. The odds of you sharing a birthday with either jumps to about 0.55%. A third and a fourth and — you get the idea. When the 253rd other person walks into that room — it’s been a few hours at that point! — only then do you have a 50% chance of having the same birthday as someone else in the room. It isn’t person 182 or 183 because some of the first two hundred-something may share birthdays. So the … Continue reading The Birthday Problem