Question 258309: Airlines find that each passenger who reserves a seat fails to turn up with probability 1/10 independently of the other passengers. So Teeny Weeny Airlines always sell 10 tickets for their 9 seat aeroplane while Blockbuster Airways always sell 20 tickets for their 18 seat aeroplane. Which is more often over-booked?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! probability that a passenger will not show up 10% of the time means the passenger will show up 90% of the time.
any plane is overbooked when at least one passenger is denied.
for the smaller plane this happens when all 10 passengers show up for the 9 seats.
the probability of this happening is .9^10 = .34867844.
for the larger plan this happens when all 20 passengers show up or when 19 of the 20 passengers show up for the 18 seats.
probability of all 20 passengers showing up for the larger plane is .9^20 = .121576655.
probability that exactly 19 passengers show up for the larger plane is .1^1 * .9^19 * C(20,1).
C(20,1) is the number of possible combinations of selecting 1 out of 20.
C(20,1) = 20!/(19!*1!) = (20*19!)/19! = 20
proability that exactly 19 passengers will show up for the larger plane is therefore .1^1 * .9^19 * 20 = .270170344.
probability that all 18 passengers or exactly 19 passengers will show up for the larger plane is equal to .121576655 + .270170344 = .391746998
based on the probabilities, the larger plane should be overbooked more often than the smaller plane.
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