--------------- 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 ?
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)\n}"
"P(Thief | Fail) = 0.9\\times\\frac{0.05}{0.14}=0.3214"
This means 32.14% of them are actually guilty.
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