SOLUTION: To reduce theft, a company proposes to screen the workers with a lie-detector test that has been proved correct 90% of the time (for guilty subjects, and also for innoc

Question 1184504: To reduce theft, a company proposes to screen the workers with a lie-detector test that has been proved correct 90% of the time (for guilty subjects, and also for innocent subjects). The company will fire all the workers who fail the test. Suppose that 5% of workers steal from time to time.
(a) If a worker is fired, what is the conditional probability he is innocent?
(b) If a worker is not fired, what is the conditional probability he is guilty?Include a probability tree for this problem.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

(a) P(worker innocent/lie-detector "guilty") = P(worker innocent ∩ lie-detector "guilty")/P(lie-detector "guilty") = 0.095/0.14 = 19/28 = 0.67857, to 5 d.p.

(b) P(worker guilty/lie-detector "innocent") = P(worker guilty ∩ lie-detector "innocent")/P(lie-detector "innocent") = 0.005/0.86 = 1/172 = 0.005814, to 6 d.p.
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