Question

A US airlines has determined that 5% of its customers do not show up for their flights. If a passenger is bumped off a flight the airline pays the customer $200. What is the expected payout of the airline, if it overbooks a 240 seat airplane by 5 percent?

Answer 1

`$0`

Explanation:

Overbooks by `5%`, therefore `240 xx 1.05 = 252` passengers booked on the airplane.
We then need to calculate `5%` of this, so `252 xx 0.05 = 12.6`.
We then need to round this to `13` as you cannot have `0.6` of a person.
`252 - 13 = 239` passengers to turn up to the flight.
`239` people is less than `240` seats available, so the expected payout is `$0`.

Answer 2

`$0`

Explanation:

Start by noting that the plane has 240 seats, and if the airline overbooked by `5%`, meaning that `105%` of the seats are booked, then `240*105%=240*1.05=252` seats were sold. Of these `252` tickets, `5%` of them will not be used, meaning that `100%-5%=95%` will be used. `252*95%=252*0.95=239.4~=240`. Since there are `240` passengers, no passengers, if everything goes according to average, no payout should be necessary.