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

Question

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 oil)=0.4

P (no oil)= 0.3

a. What is the probability of finding oil (to 1 decimal)?

b. After  feet of drilling on the first well, a soil 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)=0.4

P (Soil/no oil)= 0.2

Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).

P(Soil /High- quality oil) = ?

P(Soil/medium - quality oil)= ?

P (Soil/no oil)= ?

C. What is the new probability of finding oil (to 4 decimals)?

Explanation / Answer

a) given P(no oil) = 0.3

then P(oil) = 1-P(no oil) = 1-0.3 = 0.7

b) given P(Soil/ High - quality oil) = 0.4 , P(High quality oil) = 0.3

using baye's theorem

P(Soil) = 0.4*0.3 + 0.4 * 0.4 + 0.2*0.3 = 0.88

P(High - quality oil/ soil) = {P(Soil/ High - quality oil) * P(High quality oil)} | P(Soil) = 0.4 * 0.3| 0.88 = 0.1363

P(Soil/High - quality oil) = 1- 0.1363 = 0.8637

similarly

P(medium quality oil /soil) = 0.4 *0.4 / 0.88 = 0.1818

P(Soil/medium quantity oil) = 1-0.1818 = 0.8182

P(no oil/soil) = 0.2*0.3 / 0.88 = 0.6818

P(soil/no oil) = 1-0.6818 = 0.3182

C) P(oil) = 1- 0.3182 = 0.6818

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