7. The year is 1849, and you just came to California looking for gold. After panning all day long, you find a piece of gold but are unsure of its quality. You believe that there is a 10% chance it is high quality, a 40% chance it is medium quality, and a 50% chance it is fake gold. You can either sell your piece of gold to Sheriff Jessie for $10 guaranteed, or you can try to sell it to Sheriff Woody, who would first test the quality of the piece and then give you $40 for a high quality piece, $25 for a medium quality piece, and nothing for a fake piece of gold.

1a) Construct the decision tree. What should you do to maximize your expected monetary value?

Your friend, Buzz Goldyear, offers to test your gold piece's quality for a certain amount of money and promises that his prediction is 80% accurate. If he is inaccurate, he is equally likely to say either of the wrong quality levels. For instance, if the gold piece is high quality, he predicts that it is high quality with probability 80%, medium quality with probability 10%, and fake with probability 10%.

1. b)How much should you be willing to pay in order to have your gold tested?
2. c)What is an upper bound for what you should be willing to pay for any prediction, regardless of its accuracy?