Gold has been discovered in the Worcester Hills! So far, 100 people have tried their hands at prospecting for gold in the Worcester Hills. 20% have found it and 80% have come up dry. The average value of finding gold (among those 20 people who found it) was $1,000,000 (thats 1000 pazoozas, for those of you who are used to that form of currency.) You are thinking of trying your hand at prospecting, but it will cost you $250,000 in prospecting equipment, beer, and divorce proceedings.

1. Should you prospect and what is the EMV?

As fate would have it, Old Jack Nugget is a 95 year-old prospector who has scoured the Hills and knows where all the hidden gold is. He is willing to consult for you for $200,000 and direct you to the gold deposits. Of course, Jack is not perfect in his predictions and he also drinks a little: historically, he has been 80% accurate in predicting gold when there was gold and 90% accurate in predicting No Gold when there was No Gold.

2. Should you hire Jack?
3. What is the maximum consulting fee you would be willing to pay Jack?