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# Probability

Modern aircraft engines are very reliable. One feature contributing to that reliability is the use of redundancy, where critical components are duplicated so that if one fails, the other will work. For example, single-engine aircraft now have two independent electrical systems so that if one electrical system fails, the other can continue to work so that the engine does not fail. We will assume that the probability of electrical system failure is 0.001.

a. If the engine and aircraft has one electrical system, what is the probability that it will work?

b. If the engine and aircraft has two independent electrical systems, what is the probability that the engine can function with a working electrical system?

c. What rule of probability does this problem represent?

#### Solution Preview

(a) Probability that it will work = 1 - probability that the system will fail = 1 - 0.001 = ...

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