The Birthday Problem

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,┬áthis 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