What's the birthday paradox?

In a group of 20, there's a 50/50 chance that two people will have the same birthday; this is called the birthday paradox. Find out how it works in this podcast from HowStuffWorks.com.

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Episode Transcript

Speaker 1 (00:00):
Welcome to brain Stuff from house stuff works dot com,
where smart happens him Marshall Brain with today's question, what's
going on with the birthday paradox? You may have heard
that if there are twenty people in a room, there's

(00:21):
a fifty fifty chance that two of them will have
the same birthday. How can that be? What it really
is called the birthday paradox, and it turns out it's
useful in several different areas, for example, in cryptography and
hashing algorithms. You can try it yourself. The next time
you're at a gathering of twenty or thirty people, ask
everyone for their birthdate. It's likely that two people in

(00:43):
the group will have the same birthday. It always surprises people.
The reason this is so surprising is because we're used
to comparing our particular birthdays with other individual's birthdays. For example,
if you meet someone randomly and ask him what his
birthday is, the chance of the two of you having
the same birthday is only one out of three sixty

(01:05):
five or point to seven percent. In other words, the
probability of any two individuals having the same birthday is low.
Even if you ask twenty individual people. The probability is
still low, less than five percent, so we feel like
it's very rare to meet anyone with the same birthday
as our own. When you put twenty people in a room, however,

(01:28):
the thing that changes is the fact that each of
the twenty people is now asking each of the other
nineteen people about their birthdays simultaneously. Each individual personally has
a small chance less than five percent of success, but
everyone is trying it simultaneously. That increases the probability dramatically.

(01:50):
The next time you're with a group of twenty or
thirty people try it. You might be surprised for more
on this and thousands of other topics because at housetop
works dot com, the be