Few days ago, I came across a question for probability in one of the interview.
The same small commuter plane has 30 seats. The probability that any particular passenger will not show up for a flight is 0.1, independent of other passengers. The average fare paid by a passenger who succeeds in boarding is $100. A passenger who shows up but cannot board is given 200 dollars and a free flight later on.
Given that the airline can sell 30 + m tickets, how should the airline set m to maximize expected revenue?
I did not get how to solve this probability question. Can somebody please suggest a approach to solving this kind of questions ?