5.82 Airline overbooking.

Airlines regularly overbook flights to compensate for no-show passengers. In doing so, airlines are balancing the risk of having to compensate bumped passengers against lost revenue associated with empty seats. Historically, no-show rates in the airline industry range from 10 to 15 percent. Assuming a no-show rate of 12.5%, what is the probability that no passenger will be bumped if an airline books 215 passengers on a 200-seat plane?