eBook An oil company purchased an option on land in Alaska. Preliminary geologic

Question

eBook An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) 0.3 P(medium-quality ol)-o P(no oil)-0.2 a. What is the probability of finding oil (to 1 decimal)? 0.39 b. After 200 feet of drilling on the first well, a soill test is taken. The probabilities of finding the particular type of soil identified by the test are given below P(soil/high-quality oil)-0.4 P(soil/medium-quality oil) 0.5 P(soil lao oil) 0.1 Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals). P(high-quality oilsoil) 0.307 P(medium-quality oilsoil) 0.25 3 Ptno oilsoal) o.02 3 What is the new probability of finding oil (to 4 decimals)?

Explanation / Answer

a)P(finding oil)=1-P(no oil)=1-0.2 =0.8

b)

P(soil)=P(high quality)*P(soil|high quality)+P(med quality)*P(soil|ned quality)+P(no oil)*P(soil|no oil)

=0.3*0.4+0.5*0.5+0.2*0.1=0.39

hence P(high quality|soil)=P(high quality)*P(soil|high quality)/P(soil)=0.3*0.4/0.39=0.3077

P(med quality|soil)=0.5*0.5/0.39=0.6410

P(no oil|soil)=0.0513

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