5) Two cables are used to lift a load W (see figure below). However, normally on

Question

5) Two cables are used to lift a load W (see figure below). However, normally only cable A will be carrying the load; cable B is slightly longer than A, so normally it does not participate in carrying the load. But if cable A breaks, then B will have to carry the full load, until A is replaced. The probability that A will break is.02; also, the probability that B will fail if it has to carry the load by itself is .3. a) [5] What is the probability that both cables will fail? b) [5] If the load remains lifted, what is the probability that neither of the cables have failed?

Explanation / Answer

a) Cables A nad B works independently

So, the probability that both A and B fails = 0.02x0.3 = 0.006

b) P(road remaining lifted) = 1 - P(both cable failing)

= 1 - 0.006

= 0.994

P(neither cable failed | load remains lifted) = P(neither cables failed) / P(load remains lifted)

= P(A does not fail)/0.994

= (1 - 0.02)/0.994

= 0.9859

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