The quality control system of an automobile company runs 3 sequential tests on e

Question

The quality control system of an automobile company runs 3 sequential tests on each component that is built. Once a component fails a test, it is not allowed to take the subsequent test. Typically, 90% of the components pass the first test. Of those that pass it, 85% usually pass the second test. Finally, among the components that have also passed the second, 80% pass the third.

(a) What is the probability that a randomly chosen component passes the three tests straight?

(b) A component fails to pass the three tests straight. What is the probability that it failed the second test?

Explanation / Answer

a) probability that a randomly chosen component passes the three tests straight

=P(passes first)*P(passes second|passes first)*P(passes third|passes first two)

=0.9*0.85*0.80=0.612

b)

P(fails ) =1-P(pass the test) =1-0.612 =0.388

P(failed the second test|fails the test)=P(pass first)*P(fail second|pass first)/P(fails)

=0.9*(1-0.85)/0.388= 0.347938

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