00:01
It's given in this question that an airline sells 125 tickets for a flight that only holds 120 passengers.
00:11
We are also told that the probability for an individual passenger not showing up is 0 .1 and that the passengers behave independently.
00:22
And so we are asked what is the probability that every passenger who shows up can take the flight and what is the probability that the flight departs with empty seats.
00:31
So if we look at a, in order for every passenger to have a seat who shows up at the flight, we need at least five to not show up.
00:42
Five of the 125 passengers must not show up so that there will be at least 120 seats or more available.
00:53
So let's define a random variable that is the number of passengers who do not show up for the flight.
01:07
Now for each passenger, the probability of not showing up for the flight, flight is given as 0 .1, and we have 125 passengers because we have 125 tickets that were sold.
01:23
So that is 125 potential passengers for this flight.
01:28
Each of these potential passengers can be viewed as a bernoulli trial.
01:31
That is, there's two possible outcomes.
01:34
They either show up for the flight or they do not.
01:37
Here we're going to say that not showing up for the flight is a success, and each of the passengers can be viewed as independent from the others, since this is given in the question.
01:52
The number of successes and a given number of independent bernoulli trials is a binomial variable.
01:58
So here we can say that x is a binomial with these two parameters, p equals 0 .1 and n equals 125.
02:12
So for a we are looking for the probability that x, which is the number who did not show up, is at least 5...