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One type of passenger airplane has four engines but it can still fly with only one. Suppose each engine has probability .002 of failing during a flight.

(a) Calculate the probability of all four engines failing during the same flight. Assume independence.

(b) One accident did occur when all four engines failed. The subsequent investigation revealed that a mechanic made the same mistake servicing all four engines. Explain why your probability calculation in part (a) does not apply h ere. Because of this incident, airlines are now required to have different mechanics for each engine.

(c) Suggest another factor, other than having service performed by the same mechanic, that would violate the assumption of independence.