00:01
Here we consider a group of 27 people and we want to find the probability that at least two of them will have the same birthday.
00:09
So let's first define event a as the event in which at least two have the same birthday.
00:17
Now the probability of a can be re -expressed as 1 minus the probability of a complement.
00:26
So this is 1 minus the probability that none have the same birthday.
00:32
Now, if we assume 365 days in the year, so we ignore the leap year, february 2019, and we also assume that all days of the year are equally likely to be somebody's birthday.
00:46
So let's first consider the probability of no two people having the same birthday.
00:58
So consider the first person.
00:59
They have some birthday.
01:02
The probability that the second person has a different birthday from this person is 364.
01:10
Over 365.
01:15
That's because out of the 365 days of the year, 364 of them are different from the first person's birthday.
01:24
So let's index this as two to denote the second person...