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Over-booking

Age 16 to 18 Challenge Level:

aeroplane
An airline flies a plane with $400$ seats. Each passenger who buys a ticket arrives for the flight (that is, does not miss the flight) with probability $0.95$. If the airline sells $400$ tickets what is the expected number of empty seats?

The airline regularly books more than $400$ passengers for its flights. How many tickets can the airline sell if it wants to have to refuse passengers who arrive for the flight with tickets in no more than about two per cent of the flights?