Question: ABC Airlines operates 50 seat planes between Albany and Boston. For tomorrow's flight, it has accepted 62 reservations. From previous experience, it knows that each potential passenger with a reservation will show up for the flight with a probability of 0.78, independent of all other potential passengers.
a) Find the probability that exactly 50 passengers will show up.
b) Find the probability that all passengers who show up will get a seat on the flight.
c) What is the expected number of passengers who show up that will not get a seat on the flight?
d) What is the expected number of empty seats on the flight?
e) Explain how it is possible that the answers to parts c and d are both positive.
f) How many reservations can ABC accept if they want to be 98% sure that all passengers can be accommodated on the flight?