When someone buys a ticket for an airline flight, there is a 0.0983 probability
ID: 3257833 • Letter: W
Question
When someone buys a ticket for an airline flight, there is a 0.0983 probability that the person will not show up for the flight. A certain jet can seat 22 passengers. Is it wise to book 24 passengers for a flight on the jet? Explain.
Determine whether or not booking 24 passengers for 22 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet.
(Round to four decimal places as needed in BLANK)
A.
It is a wise decision because the probability that there are not enough seats on the jet is
BLANK. So, overbooking is not an unlikely event.
B.
It is a wise decision because the probability that there are not enough seats on the jet is
BLANK. So, overbooking is an unlikely event.
C.
It is not a wise decision because the probability that there are not enough seats on the jet is
BLANK. So, overbooking is not an unlikely event.
D.
It is not a wise decision because the probability that there are not enough seats on the jet is
BLANK. So, overbooking is an unlikely event.
Explanation / Answer
There is a 0.0983 probability that the person will not show up for the flight. Hence 1 - 0.0983 = 0.9017 is the probability that the person will show up for the flight.
There will not be enough seats on the jet if more than 22 persons show up i.e. less than 2 persons do not show up. Hence probability that less than 2 persons show up, P = (1-0.0983)^24 + 24C1*0.0983*(1-0.0983)^23 = 0.3018
It is not a wise decision because the probability that there are not enough seats on the jet is 0.3018. So, overbooking is not an unlikely event.
Option (C)
Note: I think 0.3018 is comparitively high probability. One can think this is not much high and in that case answer may change.
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