Math question please help

Question

1. US Airlines has determined that 5% of it's customers do not show up for their flights . If a passenger is bumped off a flight because of overbooking, the airline pays the customer $200. What is the expected payout by the airline, if it overbooks a 240-seat airplane by 5%?

explain with steps please

Answer 1

Hi Gary,

If 5% of US Airlines's customers do not show up for their flights, and the Airline overbooks its flights by 5%, then the Airline will actually not need to payout because if that 5% of customers do not show up for their flights, then the overbooked 5% of passengers can simply take the seats of the absent 5% and the flights will be booked to capacity without having any overbooking nor any passengers subsequently bumped off their given flight(s) in the end.

Now, if all of US Airlines's customers show up for their flights and the Airline overbooks a 240-seat airplane by 5%, the following will occur:

*5% of 240 = 12

*240 + 12 = 252

*That means that a total of 252 passengers were booked for the 240-seat airplane in question.

*Therefore, that means that 12 passengers will need to be bumped off of their flight(s).

*And, when each of those 12 passengers get paid their $200 by US Airlines, that means that the Airline will need to commit a $2,400 payout since 12 x $200 = $2,400.

Voila!

I hope this helps, Gary.