Have you ever agreed to give up your airplane ticket in return for a free ticket? Have you ever searched for the cheapest flight so that you could visit a special friend? This example provides some of the analysis that leads to results such as overbooked flights and reduced fares on certain flights.

Suppose that you are in charge of marketing airline seats for a major carrier. Four days before the flight date you have 16 seats remaining on the plane. You know from past experience data that 80% of the people that purchase tickets in this time period will actually show up for the flight.

a. If you sell 20 extra tickets, what is the probability that you will overbook the flight or have at least 1 empty seat?

b. If you sell 18 extra tickets, what is the probability that you will overbook the flight or have at least 1 empty seat?