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Problem 1 (10 marks)
An airplane has four engines. On a flight from New York to Paris, each engine has a 0.001 chance of
failing. The plane will crash if at any time two or fewer engines are working properly.
- a) What is the probability that the plane will crash?
- b) Given that engine 1 will not fail during the flight, what is the probability that the plane will crash?
- c) Given that engine 1 will fail during the flight, what is the probability that the plane will not crash?
State clearly your assumptions and show all working.
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