419 Each month a brokerage house studies various companies a

4.19 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 15 aerospace companies and 25 food retailers in the following table: Company Type Low Risk Moderate to High Risk Aerospace company 6 9 Food retailer 15 10 If we randomly select one of the total of 40 companies, find a The probability that the company?s stock is moderate to high risk given that the firm is an aerospace company. b The probability that the company?s stock is moderate to high risk given that the firm is a food retailer. C Determine if the events the firm is a food retailer and the firm?s stock is low risk are independent. Explain.

Solution

a) 9/15 = 0.6

b) 10/25 = 0.4

c) P(food retailer) = 25/40 = 0.625

   P(low risk) = 21/40 = 0.525

   P(food retailer and low risk) = 15/40 =0.375

Product of two prob = 0.625(0.525) = 0.328125

As both are not equal the events are not independent.