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). 1. 60 tickets have been sold. What is the probability that not every ticketholder will have a seat on this flight? 2. 60 tickets have been sold. What is the probability that the plane is full but no ticketholder had to be turned away? 3. 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).
1. 60 tickets have been sold. What is the probability that not every ticketholder will have a seat on this flight?
2. 60 tickets have been sold. What is the probability that the plane is full but no ticketholder had to be turned away?
3. 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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