Q3. ABC Airlines’ first class cabins have 10 seats in each plane. ABC’s overbooking policy is to sell up to 11 first class tickets, since cancellations and no-shows are always possible (and indeed are quite likely). For a given flight on ABC Airlines, there were 11 first class tickets sold. Suppose that each of the 11 persons who purchased tickets has a 25% chance of not showing up for the flight, and that the events that different persons show up for the flight are independent. (Please assume that there is no refund if the customer does not show up for the flight) (a) What is the probability that at most 5 of the 11 persons who purchased first class tickets show up for the flight? (b) What is the probability that exactly 10 of the 11 persons who purchased first class tickets show up for the flight? (c) Suppose that the cost of each first class ticket is $12,000. (Let’s assume that this $12,000 contributes entirely to profit since the variable cost associated with a passenger on a flight is close to zero.) Suppose further that any overbooked seat costs the airline $30,000, which is the cost of the free ticket issued to the passenger plus some potential cost in damaged customer relations. (First class passengers do not expect to be bumped!) What is the expected profit from first class passengers for this flight?

Q3. ABC Airlines’ first class cabins have 10 seats in each plane. ABC’s overbooking policy is to sell up to
11 first class tickets, since cancellations and no-shows are always possible (and indeed are quite likely).
For a given flight on ABC Airlines, there were 11 first class tickets sold. Suppose that each of the 11
persons who purchased tickets has a 25% chance of not showing up for the flight, and that the events
that different persons show up for the flight are independent. (Please assume that there is no refund if
the customer does not show up for the flight)
(a) What is the probability that at most 5 of the 11 persons who purchased first class tickets show up for
the flight?
(b) What is the probability that exactly 10 of the 11 persons who purchased first class tickets show up
for the flight?
(c) Suppose that the cost of each first class ticket is $12,000. (Let’s assume that this $12,000 contributes
entirely to profit since the variable cost associated with a passenger on a flight is close to zero.) Suppose
further that any overbooked seat costs the airline $30,000, which is the cost of the free ticket issued to
the passenger plus some potential cost in damaged customer relations. (First class passengers do not
expect to be bumped!) What is the expected profit from first class passengers for this flight?
(d) Suppose that only 10 first class tickets were sold. What would be the expected profit from first class
passengers for this flight?
(e) If the probability of not showing up increases, ABC Airlines may even consider sell more tickets to
increase the profit from overbooking. Now ABC Airlines is considering to sell up to 12 first class tickets.
What is the minimum probability of not showing up that may drive ABC to make this decision?