Welcome to brain Stuff production of I Heart Radio. Hi brain Stuff, I'm Lauren Vogelbaum, and this episode is another classic from our erstwhile host, Christian Sager. This one breaks down the conundrum of the birthday paradox, which isn't a true paradox, but rather a thought experiment in probability theory and a good way of demonstrating exactly how bad we humans are at probability math off the top of our heads. Hey, brain Stuff, it's Christian Sager and today's question is what
is going on with the birthday paradox. You've probably heard this one before, the idea that if there are twenty people in a room, there's a fifty fifty chance that two of them will have the same birthday. So how can this be? Well, it really is called the birthday paradox, and it turns out it's useful in several different areas, for example, in cartography and hashing algorithms. You can try it yourself the next time you're at a gathering of people. Know,
just ask everyone for their birthday. I mean, don't be creepy about it. Play cool, say you know something like I'm trying to prove this for science or whatever, and it's likely that two people in this group will have the same birthday, not around the same time, they will have the exact same day. And this really surprises people. So the reason isn't so surprising. It's because we're used
to comparing our particular birthdays with some other individuals particular birthday. So, for example, you meet somebody randomly and you ask her what her birthday is, the chance of the two of you having the same birthday is only one out of three hundred and sixty five, or four point to seven percent. In other words, the probability of any two individuals having the same birthday is low. Even if you asked twenty individual people, the probability is still low, it's less than
five percent. It's natural that we feel like it's very rare to meet anybody who has the same aimed birthday as our own. But when you put twenty people in a room, however, the thing that changes is the fact that each of these twenty people is now asking each of the other nineteen people about their birthday simultaneously. Each individual person only has a small chance, less than a five percent chance of success, but everyone's trying it at
the same time, and that increases the probability dramatically. So the next time you're with a group of twenty or thirty people, why not give it a try. You might be surprised. Today's episode was written by Ben Bolan and produced by Tyler Clang. Brain Stuff is production of I Heart Radios has to Works. For more andes and lots of other mathmagical topics, visit our home planet has toff
works dot com. Plus for more podcasts for heart Radio, visit the iHeart Radio app, Apple Podcasts, or wherever you listen to your favorite shows.