Question

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

P(high-quality oil) = 0.25 

P(medium-quality oil) = 0.20 

P(no oil) = 0.55 

If required, round your answers to two decimal places. 

(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 are as follows

P(soil | high-quality oil) = 0.20  

P(soil | medium-quality oil) = 0.80 

P(soil no oil) = 0.20 

How should the firm interpret the soil test? 

The probability of finding oil is good. Given the probability of finding good soil, the oil company is more likely to find medium-quality

 What are the revised probabilities? 

What is the new probability of finding oil?

Answer 1

a)P(finding oil)= 0.25+0.20 =0.45

b)

events	P(Ai)	P(S|Aj)	P(Ai n S)	P(Ai |S)
A1	0.25	0.2	0.05	0.15625
A2	0.2	0.8	0.16	0.5
A3	0.55	0.2	0.11	0.34375
	1	P(S)=	0.32	1

new probability of finding oil =0.15625+0.5 = 0.65625