What is the Birthday Paradox?

The so-called Birthday Paradox isn't a true paradox -- it's a fascinating example of how bad humans are at off-the-cuff probability. Tune in to learn what the Birthday Paradox is and how it works.

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Episode Transcript

Speaker 1 (00:02):
Welcome to brain Stuff from How Stuff Works. Hey, brain Stuff,
it's Christian saga 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,

(00:24):
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, you know,
just ask everyone for their birthday. I mean, don't be
creepy about it, play cool, say you know, something like

(00:45):
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,

(01:07):
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

(01:28):
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 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

(01:48):
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 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. Check out

(02:16):
the Brainsuff channel on YouTube, and for more on this
and thousands of other topics, visit how stuff works dot com.