Homework 2 Solution - Spring 2008 UGBA 143 Homework 2...

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Spring 2008, UGBA 143 Homework 2 Solution 1.  (Oil Drilling) a) We can first draw a simple probability tree as below: i.) We first want to find the probability of finding oil, given a favorable report. Recall Bayes rule,  P(A|B) = P(A & B) / P(B). In this problem, the event A is the probability of finding oil, while  event B is the probability of getting a favorable report. So we have P (finding oil & getting a favorable report) = 0.2 * 0.6 = 0.12 P (getting a favorable report) = 0.2*0.6 + 0.8*0.3 = 0.36  P (finding oil | favorable report) = 0.12/0.36 =  1/3 ii) For this part, we again use Bayes rule, we make event A to be the probability of finding oil,  while event B is the probability of getting an unfavorable report. P (finding oil & getting an unfavorable report) = 0.2*0.4 = 0.8 P (getting an unfavorable report) = 0.2*0.4 + 0.8*0.7 = 0.64 P (finding oil | unfavorable report) = 0.8/0.64 =  1/8 b) Since we know the probability of finding oil, given either favorable or unfavorable report, all we  need to find is the monetary return of drilling or not.
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