Airlines regularly overbook flights to compensate for no-show passengers. In doing so, airlines are balancing the risk of having to compensate bumped passengers against lost revenue associated with empty seats.
It was found that the average no-show rate was $12\%$. An airline books $110$ passengers on a $100$-seat plane. Assume a $12\%$ probability that a passenger will not show up for boarding.
The airline makes a profit of $\$100$ per passenger on this flight, and it estimates the cost of a bumped passenger to be $\$1000$. For this reason, the airline would like a probability of at least $0.9$ that no passenger will be bumped. How many tickets should the airline sell on this $100$-seat plane?
Could anyone guide on the solving this problem?