Answer to Question #266191 in Statistics and Probability for yousef

Question

--------------- QUESTION FOLLOWS --------------------------

a company tests its workers with a lie-detector that is correct 90% of the time and fires anyone fail the test suppose 5% of the workers are guilty of theft

1- for the workers who are fired ,calculate the percentage of them are actually guilty ?

Answer 1

P(Thief) = 0.05

P(Fail | Thief) = 0.9

$P(Fail) = (0.05)\times(0.9) + (0.95)\times(0.1) = 0.14$

$P(Thief | Fail) = P(Fail | Thief)\frac{P(Thief)}{P(Fail) }$

$P(Thief | Fail) = 0.9\times\frac{0.05}{0.14}=0.3214$

This means 32.14% of them are actually guilty.