Part II: Decision Tree (21 points) Elizabeth owns land that is inherited from her lovely grandmother who passed away three years ago. Recently she heard from the nearby land neighbors that there may be underground geothermal energy on the land. After a quick analysis she figure out that it will cost $500,000 to drill for the geothermal energy (i.e. water). If geothermal water exists on the land, Elizabeth will realize a revenue of $ 4,000,000 (i.e. not including drilling expenses). With the current information, Elizabeth estimates that there is a 0.2 probability that geothermal water is present on her land. On the other hand, she can sell the land as is for $350,000 without further information about the probability of geothermal water being present. Elizabeth also thinks about a third option, that is to perform geological tests on the land for a cost of $150,000. She determined that there is a 0.3 probability that the geological test results would be positive, after which Elizabeth can sell the land for $650,000 or drill the land with a 0.60 probability that geothermal water exists. If the test results are negative, Elizabeth can sell the land for $100,000 or drill the land with a 0.05 probability that geothermal water exists. Also, with this third option, the cost of drilling for the geothermal water is $500,000 and If geothermal water exists on the land, Elizabeth will realize the same revenue of $ $4,000,000. a) Draw the decision tree for this problem that will help Elizabeth determine the optimal decision strategy regarding her land. Make sure that the tree is well labeled, and that you include probabilities and cash flows/payoffs as appropriate. Verbally communicate the decision strategy and its expected Payoff. (Suggestion: keep track of cash/payoff flows in units of $1,000). (15 points) b) Elizabeth has some revised information concerning the accuracy of the geological test probabilities. According to this new information, the conditional probabilities regarding the quality of the geological test are: P(positive geological test geothermal water exists) = 0.95 P(negative geological test Igeothermal water does not exists) = 0.90 Please note that the prior probability of existence of geothermal water on Elizabeth's land is 0.2. Calculate the new revised probabilities (posterior probabilities) for the geothermal water to exist in the land. What would the new probabilities be for the positive and negative geological test? Show your work. Round to three decimal points. (6 points)