Airlines routinely overbook flights based on the expectation that some fraction of booked passengers

Question

Airlines routinely overbook flights based on the expectation that some fraction of booked passengers will not show up for each flight.For a particular flight that has a maximum capacity of $300$ seats, the airline has sold $312$ tickets.Assume that a booked passenger will not show for the flight with probability $5\%$ and that the number of passengers who show up for each flight follows a binomial distribution. What is the probability that there will not be enough seats for the flight? Find the probability that the flight has empty seat(s). Find the number of tickets that can be sold to ensure that the probability of overbooking is less than $3\%$.

Accepted Answer

(i) ${0.142}$ (ii) ${0.786}$ (iii) ${309}$

Prelims Revision Set: Problems involving Overbooking Q1

Prelims Revision Set: Problems involving Overbooking Q1

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