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 40 aerospace companies and 58 food retailers in the following table:

Company Type	Low Risk	Moderate to High Risk
Aerospace company	25	15
Food retailer	42	16

  
If we randomly select one of the total of 98 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.

Answer 1

Solution:
Given:

Company Type	Low Risk	Moderate to High Risk	Row Total
Aerospace company	25	15	40
Food retailer	42	16	58
Column Totals	67	31	N = 98

Part a) Find the probability that the company's stock is moderate to high risk given that the firm is an aerospace company

Let A = the company's stock is moderate to high risk and B = the firm is an aerospace company

That is we have to find: P( A | B) = ...........?

Thus using conditional probability:

where

P( A and B) = Number of the company's stock is moderate to high risk and are from an aerospace company / N

Company Type	Low Risk	Moderate to High Risk	Row Total
Aerospace company	25	15	40
Food retailer	42	16	58
Column Totals	67	31	N = 98

P( A and B) = 15 / 98

and

P(B) = Total of an aerospace company / N

P(B) = 40 / 98

Thus

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

Let A = the company's stock is moderate to high risk and C = the firm is a food retailer

Thus we have to find: P( A | C) =.........?

Thus using conditional probability:

where

P( A and C) = Number of the company's stock is moderate to high risk and are from a food retailer / N

Company Type	Low Risk	Moderate to High Risk	Row Total
Aerospace company	25	15	40
Food retailer	42	16	58
Column Totals	67	31	N = 98

P( A and C) = 16 / 98

and

P(C) = Total of a food retailer / N

P(C) = 58 / 98

Thus

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

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

Lets find: P(Aero | Low) =..........? and P( Aero) =...........?

P(Aero | Low) = Number of the company's stock is from an aerospace company and is Low Risk / Total of Low Risk

Company Type	Low Risk	Moderate to High Risk	Row Total
Aerospace company	25	15	40
Food retailer	42	16	58
Column Totals	67	31	N = 98

P(Aero | Low) = 25 / 67

P(Aero | Low) = 0.3731

and

P( Aero) = Total of an aerospace company / N

P( Aero) = 40 / 98

P( Aero) = 0.4082

Since P(Aero | Low) = 0.3731 which is not equal to P( Aero) = 0.4082,

the company type is not independent of the level of risk of the firm's stock.

That is : the company type is dependent of the level of risk of the firm's stock.