00:02
This is a classic problem known as the birthday paradox, the birthday problem.
00:06
To find the probability that at least two people of the same, or in a class of 30 share the same birthday, we can use a complement rule.
00:16
So the probability that at least two people, say at least two, share a birthday, is equal to one minus the probability that no one shares a birthday, because two would just be one match.
00:44
So let's find the probability that no one shares the same birthday.
00:53
That would be, well, the first person can have any birthday.
01:03
So there are 365 out of 365 ways to select one person.
01:12
So one.
01:14
Now the second person must have, there would only be 364 options, and they're out of the 365.
01:30
And then the second one, there would be 360 days of the year, person to third person would have 363 days to choose from out of the 365.
01:44
And this would continue on until the 30th, which would be 336 out of 365...