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 16 aerospace companies and 18 food retailers in the following table:

Company Type	Low Risk	Moderate to High Risk
Aerospace company	9	7
Food retailer	5	13

  
If we randomly select one of the total of 34 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.)

(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.)

  
(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.

Answer 1

Company Type	Low Risk	Moderate to High Risk	total
Aerospace company	9	7	16
Food retailer	5	13	18
total	14	20	34

a)

probability that the company's stock is moderate to high risk given that the firm is an aerospace company =7/16=0.4375

b)

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

=13/18 =0.7222

c)

Dependent. For two events to be independent, P(Aero | Low) = P(Aero). P(Aero | Low) =9/14=0.6429

but the P(Aero) =16/34 =0.4706
They are not equal.