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Reliability with Independence Probability of Failure in Engines

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Q: Consider a 4 engine aircraft (2 on each wing) where the probability of an engine failure is 0.002 failures per year. Assume that the probability of 1 engine falling is independent of the behavior of the others.

Determine the probability of a crash if:

a) the plane can fly on any 2 engines?

b) the plane requires at least 1 engine operating on each side in order to remain in the air?

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This solution discusses reliability with independence.

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a) Probability of engine failure = p=0.002
q=1-p=1-0.002=0.998
For plane to crash at least 3 engines should fail.
P(Crash) = P(3 engine failure) + P(4 engine failure)
P(Crash) = ...

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