Airplane Engine 2: One reason commercial airplanes have more than one engine is to

Chapter 9, Problem 8

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Airplane Engine 2: One reason commercial airplanes have more than one engine is to reduce the consequences should an engine fail during flight (Figure 9-7c). Under certain circumstances, some counterintuitive things happen when the number of engines is increased. Assume that the probability that any one engine will fail on a given flight is 0.1 (this is high, but assume it anyway). Figure 9-7c a. For a plane that has four engines, calculate the probabilities that zero, one, two, three, and all four engines fail during the given flight. Show that the probabilities add to 1, and explain the significance of this fact. b. If the plane will keep flying as long as no more than one engine fails, what is the probability that the four-engine plane keeps flying? c. Suppose a different kind of plane has three engines of the same reliability and that it, too, will keep flying if no more than one engine fails. What is the probability that the three-engine plane keeps flying? d. Based on your computations in this problem, which is safer, the four-engine plane or the three-engine plane?

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