00:01
For this question, we are told that there are 11 people in a room, and we want to find the probability that at least two share the same birthday.
00:10
So for part a, we're asked to first find the probability that 11 people have different birthdays.
00:17
So let's think of the first person that we see in the room.
00:21
They have some birthday.
00:22
So one of the 365 days of the year.
00:25
Now, we're assuming that the probability of having a birthday on any given day is equally likely amongst all 365 days.
00:34
So the first person has a birthday.
00:36
The second person, in order to not have the same birthday as the first, must have a birthday on the 364 days that are different from the first person.
00:46
So the probability that the second person has a birthday different from the day of the first person is 364 out of 365.
00:59
And if we consider the third person, the probability that that person has birthday different from the first two is the 363 remaining days divided by 365...