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12 is wrong. The correct response is: 3 passengers were overbooked. Hence, if 3 passengers (or fewer) do not show up for the flight, the
12 is wrong. The correct response is: 3 passengers were overbooked. Hence, if 3 passengers (or fewer) do not show up for the flight, the flight will be full and there will be no empty seats. If more than 3 passengers are no-shows, we will have one or more empty seats. Therefore, "one or more empty seats" is equivalent to "more than 3 no-shows". Thus, Probability (one or more empty seats) = Probability (No Shows > 3) = 1 - Probability (No Shows <= 3) = 1 - F(3), where (recall) the distribution of no-shows is Poisson with a mean of 3. Enter = 3 and Q = 3 in the "Analytics for a given Q" table for the Poisson demand model in the Newsvendor calculator. We see that F(3) = In-stock probability when Q = 3 = 64.72%. Hence, answer = 1 - F(3) = 35.28%. [Note: Probability (No Shows > 3) is also equal to the stock-out probability for Q = 3, which is 35.28%.]
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