Question

In: Statistics and Probability

Although polygraph tests are thought to be quite accurate, the results of a test may be...

Although polygraph tests are thought to be quite accurate, the results of a test may be misleading.

Suppose we have the following facts

18% of people who take a polygraph test lie.

85% of people who lie will fail the test.

7% of people who tell the truth will fail the test.

(a) If a person fails the polygraph test, what is the probability that he or she lied?

(b) If a person passes the polygraph test, what is the probability that he or she actually lied?

Expert Solution

P(people lies) = 0.18

P(fail the test | people lies) = 0.85

P(fail the test | people tell the truth) = 0.07

a) P(fail the test) = P(fail the test | people lies) * P(people lies) + P(fail the test | people tell the truth) * P(people tell the truth)

= 0.85 * 0.18 + 0.07 * (1 - 0.18)

= 0.2104

P(person lied | fails the test) = P(fail the test | people lies) * P(people lies) / P(fail the test)

= 0.85 * 0.18 / 0.2104

= 0.7272

b) P(pass the test | people lies) = 1 - P(fail the test | people lies) = 1 - 0.85 = 0.15

P(pass the test) = 1 - P(fail the test) = 1 - 0.2104 = 0.7896

P(person lied | passes the test) = P(pass the test | people lies) * P(people lies) / P(pass the test)

= 0.15 * 0.18 / 0.7896

= 0.0342

orchestra answered 2 years ago

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