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

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)?

Answer by swincher4391(1107) (Show Source): 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 =

RELATED QUESTIONS
. Airlines sell more tickets for a flight than the number of available seats... (answered by ikleyn)

I have a Statistic problem that I can't seem to figure out: In sum, here is the... (answered by stanbon)

Suppose you work for an airline and you are taking reservations for a flight on an... (answered by Boreal)

Airlines usually over-book the seats on an aircraft by a certain margin because they know (answered by ewatrrr)

Airlines overbook (sell more tickets than there are seats) flights, based on past records (answered by Boreal)

I have no idea how to go about even setting this up. Any help is greatly appreciated as... (answered by stanbon)

I took a math assessment and had difficulty solving the following problem: "Diana... (answered by MathLover1,MathTherapy)

Suppose that the probability that a passenger will miss a flight is 0.0999. Airlines do... (answered by ikleyn)

An airplane has 30 seats but some people might not show up for the flight, so they sold... (answered by stanbon)