00:01
It's data that for a certain flight route, about 2 % of the people making reservations do not show up for the flight.
00:09
An airline has sold 265 tickets for an airplane that has 255 seats.
00:16
And the random variable r is the number of people who show up for the flight.
00:23
And for part a, we're asked what is the probability that a person holding a reservation will show up for the flight.
00:30
So let's denote this p.
00:32
Well, if 2 % of the people don't show up, that means that 98 % do show up.
00:38
We can express this as a decimal, it's 0 .98.
00:44
And then for b, we're asked if n represents the 265 tickets that were sold, 265 reservations, what expression represents the probability that a seat will be available for everyone who shows up holding a reservation? a seat will be available for everyone if the number of people who show up is at most the number of seats.
01:12
So in this situation, each of the 265 reservations can be thought of as bernoulli trials having two outcomes of interest, either shows up or not.
01:22
And if we assume that their outcomes are independent, then the number of people who show up in a fixed number of independent bernoulli trials is a binomial random variable.
01:34
So r is a binomial based on 265 trials trials, and a 0 .98 probability of success on each trial.
01:44
Probability function in general for the binomial is given by this formula.
02:01
So if we want the probability that r is at most 255, this is the probability that r is any integer from 0 up to 255.
02:20
So we can write write it as the summation.
02:24
N is 265, so it's 265 choose r times 0 .98 to the exponent r times 0 .02 to the exponent 265 minus r...