Each month a brokerage house studies various companies and rates each company’s

Question

Each month a brokerage house studies various companies and rates each company’s stock as being either “low risk” or “moderate to high risk.” In a recent report, the brokerage house summarized its findings about 20 aerospace companies and 20 food retailers in the following table:

  
If we randomly select one of the totals of 40 companies

(a) Find the probability that the company's stock is moderate to high risk given that the firm is an aerospace company. (Round your answer to 4 decimal places.)

Probability        

(b) Find the probability that the company's stock is moderate to high risk given that the firm is a food retailer. (Round your answer to 4 decimal places.)

Probability          

  
(c) Determine if the company type is independent of the level of risk of the firm's stock. (Round your answers to 4 decimal places.)

Dependent. For two events to be independent, P(Aero | Low) = P(Aero). P(Aero | Low) = but the P(Aero) = . They are not equal.

Explanation / Answer

a) P(Moderate to high risk | Aerospace) = 16/20 = 0.80

b) P(Moderate to high risk | Food retailer) = 18/20 = 0.90

c) P(Aero|Low) = 4/6 = 2/3 = 0.6667

P(Aero) = 20/40 = 0.5

So they are dependent becauseP(Aero|Low) is not equal to P(Aero).

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