Airlines routinely overbook flights hoping that not everyone buying a ticket will show up. A small commuter airline always sells 60 tickets for a popular daily flight connecting two islands in the Caribbean. The aircraft for this flight only has 58 passenger seats. They also know from the past that there is a 98% chance that a ticketholder actually shows up for the flight and that it is fair to assume that whether or not a ticketholder shows up is independent of what another ticketholder does (this may not be entirely accurate since not everyone travels alone; but for the sake of this example you can assume independence). Q1: 60 tickets have been sold. What is the probability that not every ticketholder will have a seat on this flight? Q2: 60 tickets have been sold. What is the probability that the plane is full but no ticketholder had to be turned away? Q3: 60 tickets have been sold. If the airline pays $250 to every ticketholder who doesn’t find a seat because the plane is full, what can the airline expect to pay for a given flight?
Airlines routinely overbook flights hoping that not everyone buying a ticket will show up. A small commuter airline always sells 60 tickets for a popular daily flight connecting two islands in the Caribbean. The aircraft for this flight only has 58 passenger seats. They also know from the past that there is a 98% chance that a ticketholder actually shows up for the flight and that it is fair to assume that whether or not a ticketholder shows up is independent of what another ticketholder does (this may not be entirely accurate since not everyone travels alone; but for the sake of this example you can assume independence).
Q1: 60 tickets have been sold. What is the probability that not every ticketholder will have a seat on this flight?
Q2: 60 tickets have been sold. What is the probability that the plane is full but no ticketholder had to be turned away?
Q3: 60 tickets have been sold. If the airline pays $250 to every ticketholder who doesn’t find a seat because the plane is full, what can the airline expect to pay for a given flight?
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