Question

Companies use employee training for various reasons, including employee loyalty, certification, quality, and process improvement. In a national survey of companies, BI Learning Systems reported that 56% of the responding companies named employee retention as a top reason for training. Suppose 35% of the companies replied that they use training for process improvement and for employee retention. In addition, suppose that of the companies that use training for process improvement, 85% use training for employee retention. A company that uses training is randomly selected.

a. What is the probability that the company uses training for employee retention and not for process improvement?

b. If it is known that the company uses training for employee retention, what is the probability that it uses training for process improvement?

c. What is the probability that the company uses training for process improvement?

d. What is the probability that the company uses training for employee retention or process improvement?

e. What is the probability that the company neither uses training for employee retention nor uses training for process improvement?

f. Suppose it is known that the company does not use training for process improvement. What is the probability that the company does use training for employee retention?

Answer 1

let event R and P are event company gives reason for retention and process improvement

P(R)=0.56 , P(R n P) =0.35 , P(R |P) =0.85

a)

probability that the company uses training for employee retention and not for process improvement

=P(R)-P(R n P) =0.56-0.35 =0.21

b)

P(P|R) =P(R n P/P(R)=0.35/0.56 =0.625

c)

P(P) =P(R n P)/P(R|P) =0.35/0.85 =0.4118

d)

P(P u R) =P(P)+P(R)-P(P n R) =0.4118+0.56-0.35 =0.6218

e) probability that the company neither uses training for employee retention nor uses training for process improvement =1-P(P u R) =1-0.6218=0.3782

f)

P(Rc |Pc) =P(Pc n Rc)/P(Pc) =0.3782/(1-0.4118)=0.6430