In: Statistics and Probability
On any given flight, the goal of an airline is to fill the plane as much as possible, without exceeding the capacity of the plane. In order to achieve this, the airlines routinely overbook their flights in consideration of last minute cancellations. We assume that a customer cancels his/her ticket in the last minute with probability 0.08, independent of the other customers. We also assume that the airline is not able to sell more tickets in order to replace the canceled ones. What is the probability that a particular flight will be over capacity if the airline sells 304 tickets, for a plane that has a maximum capacity of 284 seats?