Question

An oil company purchased an option on land in Alaska. Pre-liminary geologic studies assigned the following prior probabilities.

P(high-quality oil)= .50

P(medium-quality oil) = .20

P(no oil) = .30

a)What is the probability of finding oil? 


b)After 200 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 follow.


P(soil | high-quality oil) = .30

P(soil | medium-quality oil) = .70

P(soil | no oil) = .20 


How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

Answer 1

a) P[ finding oil] = 1- P[ finding no oil] = 1- 0.30 = 0.70

b)

We need to find posterior probabilities , so that the company can conclude about oil using the soil information .

Let us denote : H: High quality oil

M : Medium quality oil

N: no oil

So, we need to find :  

where ,

So, posterior probabilities :