Many organizations (e.g., the CIA) hiring employees for sensitive positions give

Question

Many organizations (e.g., the CIA) hiring employees for sensitive positions give lie-detector to prospective employees. Most people don’t have a reason to lie, so that the probability that a subject is telling the truth on the test is 80%. If a subject is lying then the test is fairly effective, and detects the lie (returns a “positive”) 88% of the time, according to studies. If a person is not lying, the studies show that the test correctly returns a “negative” with probability 86%. What is the probability that a subject is lying given the lie-detector test is positive (if we take the results of the studies as facts)? For notational ease, in your answer please let L be the event that the subject is lying and let N be the event that the lie-detector test comes up negative (indicates that the subject is telling the truth).

Many organizations (e.g., the CIA) hiring employees for sensitive positions give lie-detector to prospective employees. Most people don't have a reason to lie, so that the probability that a subject is telling the truth on the test is 80%. If a subject is lying then the test is fairly effective, and detects the lie (returns a "positive") 88% of the time, according to studies. If a person is not lying, the studies show that the test correctly returns a "negative" with probability 86%. What is the probability that a subject is lying given the lie-detector test is positive (if we take the results of the studies as facts)? For notational ease, in your answer please let L be the event that the subject is lying and let N be the event that the lie-detector test comes up negative (indicates that the subject is telling the truth).

Explanation / Answer

The table is prepared to find the calculations

Prob (lying given detector positive) = 0.176/ (0.176+0.112)

=0.6111

Subject Lying Not lying Detected 0.176 0.112 Not detected 0.024 0.688 0.2 0.8

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