Question

A company believes 95% of its jobs applicants are trustworthy. the company gives everyone a polygraph test, asking "have you ever stolen anything from your workplace", to which all applicants naturally answer no. the company then uses a polygraph (lie detector) to see if they are trustworthy. suppose when a person lies, the polygraph detects the lie with probability 65%, but incorrectly identifies 15% of true statements as lies. what is the probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy

Answer 1

I'd think that the answer would be 0.15; are there any equations specified?

Answer 2

Solution:

Number of Applicants which are trustworthy= 95%

Applicants which are not trustworthy=5%

The polygraph detects the lie with probability= 65%

Probability that the statement is true, but polygraph says it's not true= 15%

Probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy=Number of Applicants which are trustworthy × Probability that the statement is true, but polygraph says it's not true

$=\frac{95\times15}{100 \times 100}\\\\= \frac{1425}{10000}\\\\=0.1425$