Question

In: Statistics and Probability

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

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.60 P(medium-quality oil) = 0.20 P(no oil) = 0.20 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 which oil? What are the revised probabilities? What is the new probability of finding oil?

Solutions

Expert Solution

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

P(high-quality oil)

=

0.50

P(medium-quality oil)

=

0.20

P(no oil)

=

0.30

If required, round your answers to two decimal places.

(a)

What is the probability of finding oil?   0.70

(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? What are the revised probabilities?

Events

P(Ai)

P(S | Ai)

P(Ai ? S)

P(Ai | S)

High Quality (A1)

0.5

0.2

0.1

0.3125

Medium Quality (A2)

0.2

0.8

0.16

0.5

No Oil (A3)

0.3

0.2

0.06

0.1875

P(S)=

0.32

What is the new probability of finding oil? 0.3125+0.5 =0.8125


Related Solutions

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following...
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 |...
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following...
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. 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. Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals). What is...
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following...
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities: P(high-quality oil) = .3 P(medium-quality oil) =.5 P(no oil) = .2 a. What is the probability of finding oil (to 1 decimal)? ______ 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 given below: P(soil/high-quality oil) = 0.3 P(soil/medium-quality oil) = 0.5...
Mobile Oil Company The Mobile Oil company owns land in Alaska that might contain natural oil....
Mobile Oil Company The Mobile Oil company owns land in Alaska that might contain natural oil. The current value of the land is worth $90,000. However, if natural oil is present at the site, the oil will be worth $800,000. If the company decides to extract the oil from the land, the company will have to pay $100,000 in drilling costs. Before drilling, the company has an option to carry out a seismic survey at the proposed drilling site. If...
An oil company owns some land that is purported to contain oil. The company classifies such...
An oil company owns some land that is purported to contain oil. The company classifies such land into four categories by the number barrels that are expected to be obtained from the well. Land category 1: a 500,000 barrel well Land category 2: a 200,000 barrel well Land category 3: a 50,000 barrel well Land category 4: a dry well. The probabilities of each type of well are given in the table below Category Land category 1: a 500,000 barrel...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil...
Investment Timing Option: Option Analysis The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT