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conditional probability with random variables

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I would like to have the response to this question in excel format so that I can see the formulas used.
The last question ask the probability that an applicant who is rejected by the polygraph is actually trustworthy. I do not quite understand this question please help/explain.

See attached file for full problem.

Lie detectors are controversial instruments barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no agreement, about the reliability of polygraph tests. Based on this research, suppose that a polygraph can detect 61% of lies, but incorrectly identifies 17% of true statements as lies. A company believes that 94% of its job applicants are trustworthy. The company gives everyone a polygraph test asking "Have you ever stolen anything from your place of work?" Naturally, all the applicants answer "No" but the polygraph identifies some of those answers as lies making the person ineligible for a job.

0.17 Polygraph says "Lie"
0.94 Trustworthy
0.83 Polygraph says "Doesn't Lie"

0.61 Polygraph says "Lie"
0.06 Dishonest
0.39 Polygraph says "Doesn't Lie"

c. What's a probability that a job applicant who is rejected by the polygraph was actually trustworthy?

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Solution Summary

This solution provides calculations for estimations of conditional probability.

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Probability (rejected & trustworthy) = 0.94*0.17
Probability (rejected & dishonest) = ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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