Question

Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable $Y$ as the number of ticketed passengers who actually show up for the flight. The probability mass function of $Y$ appears in the accompanying table. (a) What is the probability that the flight will accommodate all ticketed passengers who show up? (b) What is the probability that not all ticketed passengers who show up can be accommodated? (c) If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? What is this probability if you are the third person on the standby list?

          Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable $Y$ as the number of ticketed passengers who actually show up for the flight. The probability mass function of $Y$ appears in the accompanying table.
(a) What is the probability that the flight will accommodate all ticketed passengers who show up?
(b) What is the probability that not all ticketed passengers who show up can be accommodated?
(c) If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? What is this probability if you are the third person on the standby list?

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Added by Wesley A.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Chapter 2

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Solved by Expert Maxime Rossetti

08/04/2021

Step 1

- To find this probability, we need to sum up the probabilities of all scenarios where the number of ticketed passengers who show up is less than or equal to 50. - P(Y ≤ 50) = P(Y = 50) + P(Y = 49) + ... + P(Y = 0) - P(Y ≤ 50) = 0.10 + 0.15 + 0.20 + 0.25 + 0.20 + Show more…

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Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable $Y$ as the number of ticketed passengers who actually show up for the flight. The probability mass function of $Y$ appears in the accompanying table. (a) What is the probability that the flight will accommodate all ticketed passengers who show up? (b) What is the probability that not all ticketed passengers who show up can be accommodated? (c) If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? What is this probability if you are the third person on the standby list?

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Transcript

00:01 So i can't actually see your table, but i'm sure it's a very good table.

00:06 Y is the ticketed passengers that show up.

00:12 And we're looking at part a.

00:14 What is the probability that the flight will accommodate all ticketed passengers who show up? this is going to be the probability that y is equal to all 55 or 50.

00:28 So that's going to be 50.

00:31 And that is going to equal whatever value that is in the number.

00:34 The table.

00:35 Now for part b, what's the probability that not all ticketed passengers who show up can be accommodated? now that probability is going to be the probability.

00:49 So imagine we got 50 here and then we got an extra five here that can't show up, that they're waiting.

00:58 So we know we can get all these guys in here, but then these ones, it's a different story.

01:07 This is just going to be 100 % minus the probability of these guys over here.

01:14 So that's going to be the probability of y is greater than or equal to 51, which also can be rephrased as 51, 51, 52, 53, 54, and 55.

01:35 And then for part c, if you're the, first person on the standby list you will be the first one again on the plane if there are any seats available after all to get a passengers have been accommodated hopefully that doesn't mean that they'll onboard you in the sky um no probably does but what is the probability that you will be able to take the flights what is this probability if you are third so this is going to be so this is going to be the probability that one minus um 51 tickets are there.

02:12 So probability we have one here, an extra one there.

02:19 So if you were the first one, what is the probability that one of them doesn't show up? and then you have one here...

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