Reconsider the Goferbroke Co. case study, including its analysis in Sections 9.6 and 9.7. With the help of the consulting geologist, Jennifer Flyer now has obtained some historical data that provides more precise information than Max could supply on the likelihood of obtaining favorable seismic soundings on similar tracts of land. Specifically, when the land contains oil, favorable seismic soundings are obtained 80 percent of the time.
This percentage changes to 40 percent when the land is dry.
a. Revise Figure 9.12 to find the new posterior probabilities.
FIGURE 9.12: Probability tree diagram for the Goferbroke Co. problem showing all the probabilities leading to the calculation of each posterior probability of the state of nature given the finding of the seismic survey.

b. Use the corresponding Excel template to check your answers in part a.
c. Revise Figure 9.16 to find the new decision tree. What is the resulting optimal policy?
FIGURE 9.16: The final decision tree that records the analysis for the full Goferbroke Co. problem when using monetary payoffs.

d. Use RSPE to construct and solve this new decision tree?

Prior Probabilities Conditional Joint Probabilities Posterior Probabilities Probabilities P (state) P (finding | state) P (state and finding) P (state | finding) 0.15 = 0.5 0.3 0.25(0.6) = 0.15 ' Oil and FSS Oil, given FSS 0.6 FSS, given Oil 0.4 USS, given Oil 0.1 -= 0.14 0.25(0.4) = 0.1" Oil and USS 0.7 Oil, given USS Oil +0.15 = 0.5 0.3 4 Dry, given FSS 0.75(0.2) = 0.15 Dry and FSS FSS, given Dry 0.8 USS, given Dry 0.2 0.6 = 0.86 0.7 0.75(0.8) = 0.6 Dry and USS Dry, given USS Unconditional probabilities: P(FSS) = 0.15 + 0.15 = 0.3 P(finding) P(USS) = 0.1 + 0.6 = 0.7 0, 25 0.75 Dry Payoff -15.7 Oil (0.143) 670 800 Drill Dry (0.857) 60 -100 -130 Unfavorable (0.7) 123 90 Sell 60 270 Oil (0.5) 670 800 Favorable (0.3) Drill Dry (0.5) 270 -130 -100 123 90 Sell 60 No seismic survey 100 Oil (0.25) 700 800 Drill -100 Dry (0.75) 100 -100 90 Sell 90 Do seismic survey 0E-