The Amazing Matching Birthdays Fact
QUESTION: Suppose you are in a gathering that includes, say, three dozen folks. How likely is it that two of them have the same birthday?
Well, as it turns out, relatively decent! For now, you’ll have to take my word for it (ask if you want details), but it’s true: Believe it or not, it turns out once you hit 30 folks in a gathering, it’s a slightly better than 50-50 chance of having a set of matching birthdays!! And it goes up very rapidly after that. Get to 50 or 60 in the room and you’re almost home free.
Be sure to note: You can’t pick your day first, and then expect a good chance of a match. But (past 30 people) the chance of a match on some day is better than 50-50.
What make this so neat is not just the amazing fact. But also that the math to prove it is relatively easy to follow!! As I said, if you want more details, feel free to ask.
Fun (and pertinent) sidelight: I used to use this in my classes. If I had planned a pop quiz (which I did often early in my career), I would say “OK, write down your birthdays. If any two of them match, we’ll have a quiz.” The student breathed a sigh of relief for that day, but . . . It didn’t always work, of course, (and I didn’t always have 30 in the class), but it worked often enough to bear out the math results.
