WEBVTT - What's the birthday paradox?

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<v Speaker 1>Welcome to brain Stuff from house stuff works dot com,

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<v Speaker 1>where smart happens him Marshall Brain with today's question, what's

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<v Speaker 1>going on with the birthday paradox? You may have heard

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<v Speaker 1>that if there are twenty people in a room, there's

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<v Speaker 1>a fifty fifty chance that two of them will have

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<v Speaker 1>the same birthday. How can that be? What it really

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<v Speaker 1>is called the birthday paradox, and it turns out it's

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<v Speaker 1>useful in several different areas, for example, in cryptography and

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<v Speaker 1>hashing algorithms. You can try it yourself. The next time

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<v Speaker 1>you're at a gathering of twenty or thirty people, ask

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<v Speaker 1>everyone for their birthdate. It's likely that two people in

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<v Speaker 1>the group will have the same birthday. It always surprises people.

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<v Speaker 1>The reason this is so surprising is because we're used

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<v Speaker 1>to comparing our particular birthdays with other individual's birthdays. For example,

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<v Speaker 1>if you meet someone randomly and ask him what his

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<v Speaker 1>birthday is, the chance of the two of you having

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<v Speaker 1>the same birthday is only one out of three sixty

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<v Speaker 1>five or point to seven percent. In other words, the

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<v Speaker 1>probability of any two individuals having the same birthday is low.

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<v Speaker 1>Even if you ask twenty individual people. The probability is

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<v Speaker 1>still low, less than five percent, so we feel like

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<v Speaker 1>it's very rare to meet anyone with the same birthday

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<v Speaker 1>as our own. When you put twenty people in a room, however,

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<v Speaker 1>the thing that changes is the fact that each of

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<v Speaker 1>the twenty people is now asking each of the other

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<v Speaker 1>nineteen people about their birthdays simultaneously. Each individual personally has

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<v Speaker 1>a small chance less than five percent of success, but

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<v Speaker 1>everyone is trying it simultaneously. That increases the probability dramatically.

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<v Speaker 1>The next time you're with a group of twenty or

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<v Speaker 1>thirty people try it. You might be surprised for more

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<v Speaker 1>on this and thousands of other topics because at housetop

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<v Speaker 1>works dot com, the be