Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55

Question

Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y to be the number of ticketed passengers who actually show up for the flight. The pdf of Y appears in the table 45 46 474849 50 51 52 5354 55 0.05 0.07 0.13 0.16 0.25 0.15| 0.08 0.05 0.03 0.02 0.01 if 52 show up, 2 will be denied seats. If 48 show up, 2 on the standby can a. What is the probability that the flight will accommodate all ticketed passengers that show up to take the flight? If you are the third person on the standby list, what is the probability you will be able to take the flight? Note, if only 49 passengers show up, the first person on the standby list will be able to fly (taking the 50th and last seat) b.

Explanation / Answer

a) P(Flight will accomodate all ticketed passeengers)

= P(Less than or equal to 50 passengers showed up)

= 0.05 + 0.07 + 0.13 + 0.16 + 0.25 + 0.15

= 0.81

b) P(Third person on standy will get seat)

= P(Upto 47 persons will show up)

= 0.05 + 0.07 + 0.13

= 0.25

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