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 17 aerospace companies and 23 food retailers in the following table:

  
If we randomly select one of the total 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) Find the probability that the company's stock is moderate to high risk given that the firm is an aerospace company

Prob = 1/17 = 0.0588

(b) Find the probability that the company's stock is moderate to high risk given that the firm is a food retailer.

Prob = 17/23 = 0.7391

(c) Determine if the company type is independent of the level of risk of the firm's stock.

Dependent. For two events to be independent, P(Aero | Low) = P(Aero).

P(Aero | Low) = 16/22 = 0.7273 but the P(Aero) = 17/40 = 0.425. they are not equal

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