Question

A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about theft from previous employers, using lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. What is the probability that the lie detector says all 12 are truthful? What is the probability that lie detector says at least 1 is deceptive?

Answer 1

• p(12 are truthful) ≈ 0.0687
• p(≥ 1 are not) ≈ 0.9313

Explanation:

The probability the test says 1 is truthful is 0.8, so the probability that all 12 will be judged truthful is ...

0.8^12 ≈ 0.0687

The probability that at least one will be judged untruthful is the complement of this:

1 - 0.0687 = 0.9313

The probability that the lie detector says all 12 are truthful is about 0.0687.

The probability that lie detector says at least 1 is deceptive is about 0.9313.