00:01
Here we have a situation where an aircraft carrier made 21 reservations for a flight that has 19 seats.
00:11
18 of the reservations went to customers who are guaranteed to show up for the flight.
00:16
So that means for the other three customers, there is one seat available.
00:22
The other three customers act independently of each other, and each has a 44 % chance of showing up.
00:30
So here we have three customers, each has a probability of showing up of 0 .44.
00:40
And then we want to find the probability of an overbooking and that the flight has empty seats.
00:44
So let's define a random variable x as the number of customers, of the three remaining customers who show up for the flight.
00:57
Now each of these customers can be viewed as a bernoulli trial, which is to say there are two possible outcomes of interest.
01:03
They either show up or they do not.
01:05
And we're told that they operate independently of each other.
01:08
So the number of successes in a given number of independent or newly trials is a binomial random variable.
01:14
So here we can say x is a binomial.
01:20
And it's a binomial with these two parameters, three trials and probability of success.
01:27
.44.
01:28
The probability mass function for the binomial random variable is given by this formula.
01:46
And so now for the probability that an overbooking occurs, this will occur if more than one of the three remaining customers shows up...