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

Answer:

#$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

Answer:

#$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.