Eris Dhroso 9/28/2017 Homework #2 (Week 3) 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 (that's 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? Prospect (-250000) 1. Don't Prospect (0) Find Gold (0.2) Find NO Gold (0.8) $750000 EMV(Prospect) = (0.2)(750000)+(0.8)(-250000) = -$50000 -$250000 The right choice here is to not prospect. Chances are not very good. $0 $550000 2. Predict Right (0.8) Predict GOLD Prospect (-250000) Consult (-200000) Don't Consult (0) Don't Prospect (0) $0 Predict NO GOLD Predict Right (0.9) Predict Wrong (0.8) Predict Wrong (0.2) Predict Right (0.9) -$450000 -$450000 Predict Wrong (0.1) $550000 $750000 -$250000 EMV(GOLD) = (0.8)(550000)+(0.2)(-450000) = $350000 EMV(NO GOLD) = (0.9)(-450000)+(0.1)(550000) = -$350000