Fix Joe’s “True negative” indication (this is the probability that he correctly indicates “no treasure” when there is no treasure) at 70%, but let his “true positive” indication (this is the probability that he correctly indicates “treasure” when there is treasure) vary instead of being fixed at 85%. How accurate would his true positive indication have to be for it to make sense to hire Joe?
The problem involved a decision tree and finding the EMV. Joe cost was $200,000 and EMV was $-125,000. It was suggested to vary the 85% and solve with algebra but unsure how to proceed. Also, was mentioned SOLVER in Excel could be used.