6. (15 points) Crain Energy announced that it has discovered oil in an oil explo
ID: 3325579 • Letter: 6
Question
6. (15 points) Crain Energy announced that it has discovered oil in an oil exploration well in Northwestern India. Initial estimates placed the find between 50 million and 200 million barrels of recoverable oil. To extract the oil, there is a $400M investment in the field and a $50M remediation cost at the end of the project. Regardless of the size of the reserve, the net annual revenue of S66M per year can be expected. However, at the constant extraction rate of 10,000 barrels per day, the smaller reserve will last 14 years while the larger reserve 56 years. The chance of hitting a large reserve is 60% and the chance of hitting a small reserve is 40%. Assume the interest rate is 15%. Before making the initial investment to extract oil, Crain Energy has the option of digging an appraisal well and performs additional seismic testing to better understand the amount of reserves. Assume that the testing can be characterized as "Favorable-F" or "Unfavorable-UF". More important we know that the test will predict "Favorable" if it is actually large 90% of the time, and it will predict "Unfavorable" if the well is actually small 80% ofthe time. The corresponding decision tree is as follows: Extract without the test well Small (S) Small (S Favorable No Extraction 0 Diethe test well Large (LIU Small (SU UnfavorableTT- Note: (PA, 15%,56) 6.6640, (P/4,15%, 14)-5.7245; (P/F,15%,56): 0.0004, (PF,15%, I 4)-0.1403 No Extraction he following computations provide the necessary conditional. marginal and other probabilities. Fill in the missing entries Testing Result Favorable F Unfavorable U Joint probability Favorable E Unfavorable U Large reserve (L) 0.90 Small reserve (S) 0.200.80 Probability 0.60 040 0:10 0.54 Marginal Pr Pr(F) Pr(U) Large reserve (L) Small reserve (S) Pr(LF) Pr(SIF) P(LIU) P(S(U)Explanation / Answer
We have given table as :
Testing results
Favorable Unfavorable Total
Large reserve 0.9 0.1 1
Small reserve 0.2 0.8 1
Total 1.1 0.9 2
Table for Joint probability :
Favorable Unfavorable Marginal probability of reserve
Large reserve 0.9/2 = 0.45 0.1/2 = 0.05 1/2 =0.5
Small reserve 0.2/2 =0.1 0.8/2 =0.4 1/2=0.5
Marginal probability 1.1/2=0.55 0.9/2 =0.45 1
P( L|F) = 0.45/0.55 = 0.8182
P(S|F) = 0.1/0.55 = 0.1818
P(L|U) = 0.05/0.45 = 0.1111
P( S|U) =0.4/0.45=0.8889
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