Question

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

P(high-quality oil)	=	0.40
P(medium-quality oil)	=	0.20
P(no oil)	=	0.40

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 - Select your answer -medium-qualityhigh-qualitynoItem 2oil.
	What are the revised probabilities?
	Events P(Ai) P(S | Ai) P(Ai ∩ S) P(Ai | S) High Quality (A1) Medium Quality (A2) No Oil (A3) P(S)=

Answer 1

Ans. a)

Probability is the possibility of happening of an event or an event is likely to occur. As, it is given here that probability of finding no oil i.e P(soil | no oil) is 0.20. Then, the probability of finding oil would be = 1- probability of no oil

So, the probability of finding oil = 1 - 0.40 = 0.60 or

We can calculate in this way as well by excluding probability of finding no oil and including probability of finding oil of any quality:

Probability of finding oil = 0.40 + 0.20 = 0.60

Ans. b)

Firm can interpret that probability of finding medium quality oil is high and the oil company is more likely to find medium quality oil as its probability is highest.

Revised probabilities can be calculated as:

Events	P(Ai)	P(S | Ai)	P(Ai ∩ S) = P(Ai)*P(S | Ai)	P(Ai | S)= P(Ai ∩ S) / P(S)
High Quality (A1)	0.40	0.20	0.08	0.25
Medium Quality (A2)	0.20	0.80	0.16	0.50
No Oil (A3)	0.40	0.20	0.08	0.25
			P(S) = 0.32	= 1.0

So, new probability of finding oil = 0.25+0.50 = 0.75