Question

In a study of incentives used by companies to retain mature workers by The Conference Board, it was reported that 41% use flexible work arrangements. Suppose that of those companies that do not use flexible work arrangements, 30% give time off for volunteerism. In addition, suppose that of those companies that use flexible work arrangements, 60% give time off for volunteerism. If a company is randomly selected, determine the following probabilities:

a. The company uses flexible work arrangements or gives time off for volunteerism.
b. The company uses flexible work arrangements and does not give time off for volunteerism.
c. Given that the company does not give time off for volunteerism, the company uses flexible work arrangements.
d. The company does not use flexible work arrangements given that the company does give time off for volunteerism.
e. The company does not use flexible work arrangements or the company does not give time off for volunteerism.

Answer 1

let probability of flexible work arrangements and giving time off for volunteerism is A and B

from above P(A)=0.41 ; P(B|A)=0.60 ; P(B|A^c )=0.30

a)P(A or B) =1-P(A^c n B^c) =1-P(A^c)*P(B^c|A^c) =1-(1-0.41)*(1-0.30)=0.5870

b)P(A n B^c)=P(A)*P(B^c|A)=P(A)*(1-P(B|A))=0.41*(1-0.60)=0.1640

c)

P(A|B^c)=P(B^c|A)*P(A)/(P(B^c|A)*P(A)+P(B^c|A^c)*P(A^c)) =0.41*0.4/(0.41*0.4+0.59*0.7)=0.2842

d)

P(A^c|B^c)=1-P(A|B^c)=1-0.2842 =0.7158

e)

P(A^c u B^c) =1-P(A n B)=1-P(A)*P(B|A)=1-0.41*0.6=0.7540