On any given flight an airlines goal is to fill the plane as

On any given flight, an airline\'s goal is to fill the plane as much as possible, without overbooking. On average, 6% of customers cancel their tickets, all independently of each other.

a) What is the probability that a particular flight will be overbooked if the airline sells 304 tickets, for a plane that has maximum capacity 289 people?

Solution

No of tickets sold = 304

No of people who can sit maximum =289

The plane will be overbooked if the cancellation is 0 to 14

Consider the no of customers cancelling their tickets, as a Poisson process (approximation from binomial)

P(a particular flight will be overbooked if the airline sells 304 tickets, for a plane that has maximum capacity 289 people) = P(X <=14) where x is the no of tickets cancelled

= 1

Hence almost certain.