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 61 aerospace companies and 42 food retailers in the following table:

  
If we randomly select one of the total of 103 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.

Company Type Low Risk Moderate to High Risk Aerospace company 46 15 Food retailer 18 24

Explanation / Answer

Solution:-

(a) The probability that the company's stock is moderate to high risk given that the firm is an aerospace company is 0.2459.

Number of companies that are an aerospace company = 61

Number of Moderate to High Risk stock in aerospace company = 15

The probability that the company's stock is moderate to high risk given that the firm is an aerospace company = 15/61 = 0.2459

(b) Find the probability that the company's stock is moderate to high risk given that the firm is a food retailer is 0.5714.

Number of companies that are Foodstock company = 42

Number of Moderate to High Risk stock in Foodstock company = 24

The probability that the company's stock is moderate to high risk given that the firm is an aerospace company = 24/42 = 0.5714

c) Dependent

For independent

P(Aero | Low) = P(Aero). P(Aero | Low)

P(Aero | Low) = 46/64 = 0.71875

P(Aero) = 0.4466

Since they are not equal, so two events are dependent.

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