00:01
In this exercise, we are told that in a certain zoom session, there are 500 attendees including yourself.
00:08
So what is the probability that exactly one other person has the same birthday as you? so we can view this as a sample or a number of trials of 499.
00:22
So other than yourself, there are 499 people that may or may not have the same birthday as you.
00:32
For a randomly selected person, the probability that that person has the same birthday, as you is 1 out of 365.
00:42
That's ignoring february 29th and the specific year of your birth.
00:50
So we can say x is the number of people on the zoom call that have the same birthday as you.
01:09
So x is a binomial random variable with n and p as shown here.
01:21
The probability mass function for the binomial is given by this formula.
01:25
And so we want the probability that x is exactly 1.
01:47
So using the binomial probability mass function, that's 499 choose 1 times 1 over 365 to the exponent 1 times 364 over 365 to the exponent 498...