00:01
In this scenario, we have a small plane which has seats for 11 people, and the carrier booked 14 reservations for this flight.
00:11
Now, 10 of the reservations went to customers who are guaranteed to show up, and four went to customers who have a 48 % chance of showing up.
00:21
So we have four special customers, and for each of them, the probability of showing up is 0 .48.
00:29
And these customers are independent from each other.
00:33
So the probability of one showing up or the outcome of one showing up has no bearing on the others.
00:39
And so we're asked two questions.
00:40
The first is the probability that an overbooking occurs.
00:44
So there are 11 seats.
00:46
10 people are guaranteed to show up.
00:49
So that means out of the remaining four, at most one can show up without an overbooking.
00:56
So that means we have an overbooking if two or more show.
01:00
So let's define the random variable x as the number of the four that show up for the flight.
01:14
Each of these four can be viewed as a bernoulli trial.
01:17
That is, there's two possible outcomes of interest that either show up or they do not.
01:21
And since they operate independently from each other, the number of successes in the given number of independent bernoulli trials is a binomial random variable...