An airline knows that 5 percent of the people making reserva

An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up?

Solution

We need to account for only two cases when there are more people than seats. The probability that all 52 people show up is (0.95)⁵² and the probability that 51 people show up is 52(0.95)⁵¹(0.05) because any one of the 52 people might not show up. Therefore, our desired probability is

1 (0.95)⁵² 52(0.95)⁵¹(0.05)