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?

2 Answers
May 8, 2017

$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.

May 8, 2017

$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.