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, $20\%$ 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 volunteer ism.

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.

a$.$

$($Round your answer to $3$ decimal places, e$.$g$.0\mathrm{.}215.)$

b$.$

$($Round your answer to $3$ decimal places, e$.$g$.0\mathrm{.}215.)$

c$.$

$($Round your answer to $4$ decimal places, e$.$g$.0\mathrm{.}2153.)$

d$.$

$($Round your answer to $4$ decimal places, eg$.0\mathrm{.}2153.)$

e$.$

$($Round your answer to $3$ decimal places, eg$.0\mathrm{.}215.)$