Question

The next three questions refer to the following information 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).

60tickets have been sold. if the airline pays $250 to every ticketholder who deson't find a seat because the plane is full.

what can the airline expect to pay for a given flight?

Answer 1

wt X % No of passengers shows up for the fight. It follows binomial dist where n=60, p=0.58 -- P(X=) ppcl-)926.)(0.989% (0.02)60-* of Y: No of passengers who couldn't find the seat. then = x-58 += 59,60 Ply=1) - PCX-59)= 0.364351, PCY=2)=P(x=60)= 0.303626 ': Expected no of passengers who couldn't find seat ECY)= *P(Y=1) +2» PCY=2)= 0.971602 .. Expected amount to be paid$250 x 0.971602 - $242.9006