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Reserving a seat on an airplane isn’t exactly a sure thing. Airlines routinely sell more tickets for a flight than there are available seats, a process called overbooking. If too many people show up at the gate, then some passengers will have to get bumped to a different flight. It can be extremely frustrating. So, why would airlines put their customers through such pain?

In this lesson, students use probability and expected value to investigate the overbooking phenomenon and why airlines make the decisions they do.

Students will

  • Use average passenger “no-show” rate to calculate potential lost revenue for a typical flight
  • Given a percentage of no-show passengers, calculate an overbooking level that leads to full average flights
  • Reason about mean rates to estimate the percentage of flights that have to bump passengers
  • Calculate the probability that an overbooked flight will be exactly full on takeoff
  • Use a binomial distribution to calculate expected cost to an airline due to compensating bumped passengers
  • Discuss considerations for airlines as they develop policies on overbooking flights

Before you begin

Students should be able to calculate binomial probabilities given a rate of success or failure and the number of trials: for instance, if the probability of success is 0.9, then the probability of 150 successes out of 166 trials is given by 166C150 × 0.9150 × 0.116. They should also be able to use probabilities to calculate expected value as a weighted average.

Common Core Standards

Content Standards
Mathematical Practices