Approximately 70% of the State of Pennsylvania Sits on a Shale

question 98

Short Answer

Approximately 70% of the state of Pennsylvania 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.

---

Definitions:

Greatest Good

A principle suggesting that actions should be evaluated based on their ability to produce the maximum amount of happiness or benefit for the greatest number of people.

Trap Of Rationalization

The justification of questionable behavior with seemingly reasonable excuses, obscuring true motives or flaws.

Self-Deception

A psychological process where an individual convinces themselves of a false reality to avoid facing uncomfortable truths.

Nonverbal Facial Expression

Facial gestures and movements that are used to convey emotions or messages without speaking.