Airlines sometimes overbook flights. Suppose that for a plane with S0 seats, 55

Question

Airlines sometimes overbook flights. Suppose that for a plane with S0 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. y45 46 47 48 49 50 51 52 53 54 55 py) 0.06 0.10 0.11 0.14 0.24 0.18 0.06 0.05 0.03 0.02 0.01 (a) What is the probability that the flight will accommodate all ticketed passengers who show up? 0.83 (b) What is the probability that not all ticketed passengers who show up can be accommodated? 0.17 (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 passengens have been accommodated), what is the probability that you will be able to take the fight? 0.66 what is this probability if you are the third person on the standby list? 0.28

Explanation / Answer

c) If we are first in the standby list, this means that we would be able to get a seat when either 54 or less than 54 passengers show up. Therefore the probability here is computed as: ( because we are initially 51st on the list and if 1 or more persons dont show up then we will be the first one to get the seat )

P(X < = 54 ) = 1- P(X=55) = 1 - 0.01 = 0.99

Therefore 0.99 is the required probability here.

d) Probability to get a seat if we are third person on the list = Probability that 3 or more people dont show up

P(X < = 52 ) = 1 -P(X=55) -P(X=54) - P(X-53 ) = 1 - 0.01 - 0.02 - 0.03 = 0.94

Therefore 0.94 is the required probability here.

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