Airlines sometimes overbook flights (anticipating that some passengers will not

Question

Airlines sometimes overbook flights (anticipating that some passengers will not show up). Suppose that an airline took 110 reservations for a plane with 100 seats.

Let X= the number of people with reservations who actually show up for the flight.

The Probability distribution of X is: x = 95, 96, 97, 98 , 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109 p(X) = 0.05, 0.10, 0.12, 0.14, 0.24, 0.17, 0.06, 0.04, 0.03, 0.02, 0.01, 0.007, 0.006, 0.004, 0.003 a) What is the probability that everyone who showed up for the flight can get on the flight?

b) What is the probability that at least three passengers will not be able to get on the flight?

c) If you don't have reservations and you are number 2 on the stand-by list, what is theprobability that you will be able to get on this flight?

Explanation / Answer

(a) probability that everyone who showed up gets the seat = P(X<=100)= 0.82

(b)probability that at least three passengers will not be able to get on the flight = P(X>=103) = 0.177

(c)theprobability that you will be able to get on this flight = P(X=95,96,97,98) = 0.41

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