You have gotten tired of working for a living and have taken a brainwave to buy a salvage vessel, cruise to Bermuda, and dive for sunken treasure to become rich. The cost of the vessel, diving gear, a crew, and insurance against "the bends" is $200,000. But the potential payoff is huge: $2 million if you actually find and recover the treasure. Now historically, only 1 out of every 20 treasure hunters like you has ever hit pay dirt.

1) Should you invest in diving for treasure, or suck it up and go back to your regular job?

2) What is the expected value of Perfect Information on whether there is treasure or not?

You know of a dude named "Salty Joe McSharkbait." Salty Joe has cruised the waters off Bermuda for 80 years. He knows where all the wrecks are, which have been plundered, and which have treasure just waiting to be recovered. He has offered to sell you his advisory services for $25,000. But, because Joe is 90 years old, his memory is not perfect. If there is treasure at a particular site, he will indicate so 85% of the time. If there is no treasure, he will correctly indicate that 70% of the time. If Joe Predicts treasure, you will go for it, but if he predicts no treasure, you will forego the whole affair and get back to your regular job.

3) Should you hire Joe? Why or why not? What is the Expected Monetary Value (EMV) of hiring Joe?

4) 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?