SOLUTION: Airlines sell more tickets for a flight than the number of available seats (overbooking). They do this because they know from past experience that only 90% of ticketed passengers
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Question 671680: Airlines sell more tickets for a flight than the number of available seats (overbooking). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.
(a) A plane has 6 seats. If the airline sells 8 tickets for a flight, what is the probability that the flight will be overbooked (the number of passengers who show up is greater than the number of available seats)?
(b) A plane has 325 seats. If the airline sells 350 tickets for a flight, what is the probability that the flight will be overbooked (the number of passengers who show up is greater than the number of available seats)?
You can put this solution on YOUR website! Let p (not showing) = .10
1) Let n = 8. This situation satisfies the binomial distribution.
Choose 0 to not show up:
(8 choose 0) (.1)^0 (.9)^8
Choose 1 to not show up:
(8 choose 1) (.1)^1 (.9)^7
Adding this we get:
(.9)^8 + 8 * .1 * .9^7 =
2) Let n = 350
In the same way:
(350 choose 0) *(.1)^0 (.9)^349 + (350 choose 1) * (.1)^1 (.9)^348 + ... + (350 choose 24) *(.1)^24 (.9)^326 =
