In a certain four-engine vintage aircraft, now quite unreliable, each engine has a 15% chance of failure on any flight, as long as it is carrying its one-fourth share of the load. But if one engine fails, then the chance of failure increases to 30% for each of the other three engines. And if a second engine fails, each of the remaining two has a 45% chance of failure. Assuming that no two engines ever fail simultaneously, and that the aircraft can continue flying with as few as two operating engines, find the probability for no engine failures.

In a certain four-engine vintage aircraft, now quite unreliable, each engine has a 15% chance of failure on any flight, as long as it is carrying its one-fourth share of the load. But if one engine fails, then the chance of failure increases to 30% for each of the other three engines. And if a second engine fails, each of the remaining two has a 45% chance of failure. Assuming that no two engines ever fail simultaneously, and that the aircraft can continue flying with as few as two operating engines, find the probability for no engine failures.

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a certain four-engine vintage aircraft, now quite unreliable, each engine has a

15%

chance of failure on any flight, as long as it is carrying its one-fourth share of the load. But if one engine fails, then the chance of failure increases to

30%

for each of the other three engines. And if a second engine fails, each of the remaining two has a

45%

chance of failure. Assuming that no two engines ever fail simultaneously, and that the aircraft can continue flying with as few as two operating engines, find the probability for no engine failures.

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