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The Goferbroke Company develops oil wells in unproven territory. A consulting geologist has reported that there is a 20% of oil on a particular tract of land. Drilling for oil on this tract would require an investment of about $100,000. If the tract contains oil, it is estimated that the net revenue generated would be approximately $800,000. Another oil company has offered to purchase the tract of land for $90,000 Payoff Table (Profit in $Thousands) State of Nature Alternative (Sl=Oil) (S2=Dry) Drill for oil (di) 700 -100 Sell the land (d2) 90 90 Prior probability 0.20 0.80 Goferbroke can obtain improved estimates of the chance of oil by conducting a detailed seismic survey of the land, at a cost of $10,000. Possible findings from a seismic survey F. Favorable seismic soundings, oil is fairly likely. U: Unfavorable seismic soundings, oil is quite unlikely. Conditional Probabilities State of Nature Oil (SI) Favorable (F) Unfavorable(U) P(FISI) = 0.15 PUISI) = 0.85 P(F | S2) = 0.40 P(UI S2) = 0.60 Dry (S2) a. Calculate the posterior probabilities by completing the following tables: (Round your answers to 3 decimal places.) P(SjF) sj P(s)) P(FS) P(sj) P(F| Sj) SI 0.20 0.15 P(SjF) S2 0.80 0.40 11.00 P(SjU) si P(sj) Pulsi) P(si) P(US) SI 10.20 P(Slo) 0.85 S2 10.80 0.60 1.00 b. Incorporate the prior and posterior probabilities in the given decision tree for Goferbroke Company here. Then answer to the following questions: The optimal policy is If the result is favorable - If the result is unfavorable b. Incorporate the prior and posterior probabilities in the given decision tree for Goferbroke Company here. Then answer to the following questions: The optimal policy is If the result is favorable If the result is unfavorable The expected payoff (including the cost of the seismic survey) is (in $ thousands)