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'Over-booking' printed from http://nrich.maths.org/
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?