Final answer:
To calculate the probability that all 10 passengers show up on a 9-seat airplane, we multiply the probability of each passenger showing up (0.88) by itself 10 times. This gives us an approximate probability of 26.84% that not enough seats will be available, which is not one of the provided answer choices.
Step-by-step explanation:
The question deals with the probability of an overbooking scenario on an airline flight. Given that the airline has a history of 88.0% of booked passengers actually arriving, and with an overbooking of one person on a 9-seat airplane, we need to find the probability of all 10 booked passengers arriving, thus resulting in not enough seats available.
The question can be solved using the binomial probability formula, but in this case, we can calculate the probability of all 10 passengers showing up as the product of each passenger showing up independently, because we are dealing with a single event -- all passengers arriving. The probability of one passenger not showing up is 1 - 0.88 = 0.12, and thus the probability of a passenger showing up is 0.88. Since the passengers arrive independently, the probability that all 10 passengers show up is 0.8810.
Using a calculator, we find that 0.8810 ≈ 0.2684, or 26.84%. Hence, the probability that there will not be enough seats available is 26.84%. This answer isn't provided in the options, so the student needs to reevaluate the calculation or the possible answers provided.