Question

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.30 P(medium-quality oil) = 0.20 P(no oil) = 0.50 If required, round your answers to two decimal places. (a) What is the probability of finding oil? 0.50 (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 oil. What are the revised probabilities? Events P(Ai) P(S | Ai) P(Ai ? S) P(Ai | S) High Quality (A1) 0.30 0.2 0.010 0.3125 Medium Quality (A2) 0.2 0.8 0.16 0.5 No Oil (A3) 0.50 0.2 0.060 0.1875 1 P(S)= 0.32 1 What is the new probability of finding oil? 0.3130

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

P(high-quality oil) = 0.30
P(medium-quality oil) = 0.20
P(no oil) = 0.50

If required, round your answers to two decimal places.

(a) What is the probability of finding oil?
0.50

(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 oil.

What are the revised probabilities?

Events P(Ai) P(S | Ai) P(Ai ? S) P(Ai | S)
High Quality (A1) 0.30 0.2 0.010 0.3125
Medium Quality (A2) 0.2 0.8 0.16 0.5
No Oil (A3) 0.50 0.2 0.060 0.1875
1 P(S)= 0.32 1

What is the new probability of finding oil?
0.3130

Show more…

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

P(high-quality oil) = 0.30
P(medium-quality oil) = 0.20
P(no oil) = 0.50

If required, round your answers to two decimal places.

(a) What is the probability of finding oil?
0.50

(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 oil.

What are the revised probabilities?

Events P(Ai) P(S | Ai) P(Ai ? S) P(Ai | S)
High Quality (A1) 0.30 0.2 0.010 0.3125
Medium Quality (A2) 0.2 0.8 0.16 0.5
No Oil (A3) 0.50 0.2 0.060 0.1875
1 P(S)= 0.32 1

What is the new probability of finding oil?
0.3130

Added by David S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ana Carolina Da Cruz

10/05/2022

Step 1

- Prior probabilities: - \( P(\text{high-quality oil}) = 0.30 \) - \( P(\text{medium-quality oil}) = 0.20 \) - \( P(\text{no oil}) = 0.50 \) Show more…

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An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities: P(high-quality oil) = 0.30 P(medium-quality oil) = 0.20 P(no oil) = 0.50 (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 oil. What are the revised probabilities? Events P(Ai) P(S | Ai) P(Ai ∩ S) P(Ai | S) High Quality (A1) 0.30 0.2 0.010 0.3125 Medium Quality (A2) 0.2 0.8 0.16 0.5 No Oil (A3) 0.50 0.2 0.060 0.1875 P(S)= 0.32 What is the new probability of finding oil?

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Transcript

00:01 A, we need to find what is the probability of like finding oil.

00:05 So basically, this is given by one minus the probability of no oil, no finding oil.

00:12 So basically, we have that we are going to find no oil, any oil, as like a 0 .5.

00:21 So this means that the probability of finding oil is 0 .5 as well.

00:26 So now let's consider that we have that the probability that are tests here of the soil given that we have a high quality oil is 0 .2.

00:40 So again, the test given that we have a median quality is 0 .80 and the test when we don't have any oil is 0 .2.

00:54 So we also have, like in the first part of the question, the marginal probability of like having a high quality oil, which is 0 .3.

01:05 The probability of having a median quality is 0 .2.

01:10 And the probability of no oil here that we already used is 0 .5.

01:16 So first, looking at this here, these probabilities, we first need to say, given that the probability of finding good soil, the oil company is more likely to find which kind of oil that we have.

01:35 So basically, we should look at the one that is like the largest.

01:40 So there will be this one here.

01:42 So for the first part in the second item, we should like put that the company is more likely to find a median quality because it is the one that has the highest.

01:54 Highest probability.

01:57 Now we should compute the revised probabilities.

02:01 So we have a table, which we have this order, like high quality is a1, median quality is a2, then no oil is a3, and we have here the probabilities of each one of this.

02:21 So from the question we have, these probabilities the same as this one here.

02:25 So we're going to put each one of this here.

02:27 So 0 .3, 0 .2 and 0 .5.

02:32 And we have a space here to express the sum...

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