The HR department is trying to fill a vacant position for a job with a small talent pool. Valid applications arrive every week or so$,$ and the applicants all seem to bring different levels of expertise. For each applicant, the HR manager gathers information by trying to verify various claims on the candidate's r$$sum$,$ but some doubt about $$fit$$ always lingers when a decision to hire or not is to be made.

Suppose that hiring an employee who is a bad fit for the company results in an error cost of $$900,$ but failing to hire a good employee results in an error cost of $$200$ to the company. Although it is impossible to tell in advance whether an employee is a good fit, assume that the probability that an applicant is a $$good fit$$ is $0\mathrm{.}4,$ while the probability that an applicant is a $$bad fit$$ is $10\mathrm{.}4=0\mathrm{.}6$

$.$ Hiring an applicant who is a good fit, as well as not hiring an applicant who is a bad fit, results in no error cost to the company.