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To reduce theft among employees, a company subjects all employees to lie-detector tests and then res all employees failing this test. In the past, the test has been proven to correctly identify guilty employees 95% of the time; however 8% of the innocent also fail the test. Suppose that 20% of the employees are actually guilty.

What percentage of employees fail the test? What percentage of those fired were innocent?

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    $\begingroup$ en.wikipedia.org/wiki/Bayes'_theorem $\endgroup$ – Ilya Sep 21 '11 at 14:59
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    $\begingroup$ It's worth noting, though irrelevant to your problem, that 95% is much higher and 8% much lower than the actual rates for polygraph tests. No comment on the 20%! $\endgroup$ – Charles Sep 21 '11 at 18:01
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Hint: Out of 100 employees, how many are guilty? How many innocent? Of the innocent, how many fail?

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