An airline accepts 10 reservations for a flight on a small plane with 8 seats. They know that 5 reservations go to passengers who always show up. Each of the other passengers shows up with probability 0.5, independently.
(a) Find the probability that the flight is overbooked.
(b) Suppose that the airline will cancel the flight unless there are at least 7 passengers. What is the probability that the flight gets cancelled.
(c) What is the expected number of passengers turned away due to cancellation?
(d) What is the expected number of passengers turned away due to overbooking?
(e) Suppose that the airline has to pay $150 to each person who cannot fly because his flight is overbooked, and pays $100 to each person (who shows up) whose flight gets cancelled. How much should the airline charge per ticket to expect to break even?