Question

The good operation of a machine requires that four component parts do not fail. Each component part has a 0.01 probability of failing. The chances of failure for any two parts are probabilistically independent. a What is the probability that the first and second component both fail? b. What is the probability that one or both of the first and second component fail? c. Given that the first component fails, what is the probability that the second component fails? T T T Arial Path: p Words:0

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Answer #1

a) P(first and second component both fail) = 0.01 x 0.01 = 0.0001

b) P(one or both of the first and second components failed) = 1 - P(both components didnt fail)

= 1 - 0.99x0.99

= 0.9801

c) P(second component fail | first component fail) = 0.01

(because the events are independent)

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