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5.Approximately 70% of a state sits on a shale formation fromwhich natural gas may be extracted. If a geological test ispositive, it has an 80% accuracy rate in cor...

Question

5.Approximately 70% of a state sits on a shale formation fromwhich natural gas may be extracted. If a geological test ispositive, it has an 80% accuracy rate in correctly identifying aproductive drilling site (shale is under the ground). If there isno shale under the ground, geological testing is falsely positivewith a probability of 20%. Suppose the result of the geologicaltest comes back positive (the test says there is shale under theground). It is most important for us to know the probabilit

5.Approximately 70% of a state sits on a shale formation from which natural gas may be extracted. If a geological test is positive, it has an 80% accuracy rate in correctly identifying a productive drilling site (shale is under the ground). If there is no shale under the ground, geological testing is falsely positive with a probability of 20%. Suppose the result of the geological test comes back positive (the test says there is shale under the ground). It is most important for us to know the probability that there is indeed shale under the ground given a positive geological test result. Find this probability and briefly discuss your results. ============================================================ An investor in Facebook is worried the latest management earnings forecast is too aggressive and the company will fall short. His favorite analyst that covers Apple is going to release his report on Facebook the week before the earnings announcement. Report stands for the analyst’s report, and Forecast stands for the earnings announcement. Prior Probabilities Conditional Probabilities P(Good Report) = 0.2 P(Below Forecast | Good Report) = 0.1 P(Medium Report) = 0.5 P(Below Forecast | Medium Report) = 0.4 P(Bad Report) = 0.3 P(Below Forecast | Bad Report) = 0.9 What is the probability the earnings announcement is below the forecast? Briefly Discuss



Answers

An oil company purchased an option on land in Alaska. Preliminary geologic studies
assigned the following prior probabilities.
$\begin{array}{l}{\text { a. What is the probability of finding oil? }} \\ {\text { b. After } 200 \text { feet of drilling on the first well, a soil test is taken. The probabilities of find }} \\ {\text { ing the particular type of soil identified by the test follow. }}\end{array}$
$$\begin{aligned} P(\text { soil } | \text { high-quality oil }) &=.20 \\ P(\text { soil } | \text { medium-quality oil }) &=.80 \\ P(\text { soil } | \text { no oil }) &=.20 \end{aligned}$$
How should the firm interpret the soil test? What are the revised probabilities, and what is
the new probability of finding oil?


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