Lipossig

2020-12-29

An option on land in Alaska was bought by an oil company. The following prior probabilities were assigned by preliminary geologic studies.
$PP\left(\text{high-quality oil}\right)=.50P\left(\text{medium-quality oil}\right)=.20P\left(\text{no oil}\right)=.30$
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 follow.
$P\left(\text{soil | high-quality oil}\right)=.20P\left(\text{soil | medium-quality oil}\right)=.80P\left(\text{soil | no oil}\right)=.20$
How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

Alannej

Given:
$P\left(\text{no oil}\right)=0.30$
a. Complement rule:
$P\left(\text{not}A\right)=1-P\left(A\right)$
Use the complement rule:
$P\left(\text{oil}\right)=1-P\left(\text{no oil}\right)=1-0.30=0.70$
b. We are most likely to find the type of soil, when we have found medium-quality oil.
The probabilities remain unchanged> becase the given probability only effect the probability of finding soil and not the probability of finding oil.

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