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Chapter 4

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.

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6.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.Reportstands for the analyst's report, andForecaststands 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 isbelowthe forecast? Briefly Discuss

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7.An investor is keeping a careful eye on the real estate markets in Las Vegas and Florida. The following are her predictions for the real estate market in 2017.

With 0.32 probability, foreclosures will increase in Las Vegas.

With 0.46 probability, foreclosures will increase in Las Vegas or Florida.

With 0.27 probability, foreclosures will increase in Las Vegas and Florida.

What is the probability that foreclosures willincreasein Florida given that they increased in Vegas? Briefly discuss why.

8.Restaurants in California, Florida, and New York want diners to experience eating in pitch darkness to heighten their senses of taste and smell. Suppose 400 people were asked, "If given the opportunity, would you eat at one of these restaurants?" The accompanying contingency table, cross-classified by age, would be produced.

18-29

30-44

45-64

65+

Yes

50

39

76

65

No

50

61

24

35

a. What is the probability that a respondent would eat at one of these restaurants?

b. What is the probability that a respondent would eat at one of these restaurants or is in the 30-44 age bracket?

c. Given that the respondent would eat at one of these restaurants, what is the probability that he or she is in the 30-44 age bracket?

d. Is whether a respondent would eat at one of these restaurants independent of one's age? Explain using probabilities and discuss results.

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9. As a company manager for ABC Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.25.

a.

If you get a promotion, what is the probability that you will also get a raise?

b.

What is the probability that you will get a raise?

c.

Are getting a raise and being promoted independent events? Explain using probabilities.

d.

Are these two events mutually exclusive? Explain using probabilities and discuss results.

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