An oil company believes that the probability of existence of an oil deposit in a
ID: 3205905 • Letter: A
Question
An oil company believes that the probability of existence of an oil deposit in a certain drilling area is 0.16. Suppose it would cost $200,000 to drill a well. If an oil deposit does exist, the company's profit will be $1,400,000 (the drilling costs not included). A seismic test that would cost $40,000 is being considered to clarify the likelihood of the presence of oil. The proposed seismic test has the following reliability: when oil does exist in the testing area, the test will indicate so 95% of the time; when oil does not exist in the test area, 19% of the time the test will erroneously indicate that it does exist. There are four possible "states of nature":
1 = an oil deposit does exist and the test result is positive,
2 = an oil deposit does exist, but (and) the test result is negative,
3 = an oil deposit does not exist, but (and) the test result is positive,
4 = an oil deposit does not exist and the test result is negative.
P(1) = 0.1520 , P(2) = 0.0080 , P(3) = 0.1596 , P(4) = 0.6804 .
b)Suppose the test shows presence of oil. What is the probability that an oil deposit does exist?
c) Construct the payoff table (profit table) for this problem. That is, find the company's profit for each possible action and each possible state of nature. Enter integers (can be positive or negative) in the following table.
d) Find the expected payoff (expected profit, EP) for both actions and determine the optimal action.
1 (Oil +) 2 (Oil -) 3 (No Oil +) 4 (No Oil -) a1drill w/o test a2
drill onif if test +
Explanation / Answer
b) If the test shows presence of oil, the probability that an oil deposit does exist = O1 = 0.1520
c) Profit after drilling costs are added = (1,400,000- 200,000) = 1,200,000
d) Expected payoff
probability of oil existing = 0.16
Also given, the test will indicate so 95% of the time;
when oil does not exist in the test area, 19% of the time the test will erroneously indicate that it does exist.
Let,
for calculation understanding where A = 1200000
Now, expected payoff = A * 0.16 + B* 0.16 + C * 0.84 + D * 0.84 + E * 0.16* 0.95* 0.1520 + F * 0.16 * 0.95* 0.008 + G * 0.84 * 0.19 * 0.01596 + H * 0.84 * 0.19 * 0.6804
From the above two decisions it is evident that seismic testing doenot yeild profits.
O1(oil+) O2(Oil-) O3(Oil+) O4(Oil-) a1, drill without test 1200000 1200000 -200000 -200000 a2, drill only if test (+) 1160000 0 -240000 0