Use Bayes' Theorem to Find the Indicated Probability

Multiple Choice

Use Bayes' theorem to find the indicated probability.
-Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 63% of lies are identified as lies and that 16% of true statements are also identified as lies.
A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job application?". Suppose that 90% of the job applicants tell the truth during the polygraph test.
What is the probability that a person who fails the test was actually telling the truth?

A) 0.438
B) 0.696
C) 0.304
D) 0.16