In the last decade, increasingly more employees have been offered a variety of health care plans to choose from. This is a direct result of the growing prevalence of preferred provider organizations

(PPOs) and health maintenance organizations

(HMOs). PPOs permit employees to choose their health care provider. but offer financial incentives when designated doctors and hospitals are chosen.

HMOs offer prepaid health care from a particular set of providers (Monthly Labor Review, Oct.

1995). A survey of 100 large. 100 medium, and 100 small companies that offer their employees HMOs, PPOs, and fee-for-service plans was conducted;

each firm provided information on the plans chosen by their employees. These companies had a total employment of 833,303 people. A breakdown of the number of employees in each category by firm size and plan is provided in the table.

One employee from the 833,303 total employees is to be chosen at random for further analysis.
Define the events A and B as follows:
A: (Observe an employee that chose fee-for-service)
B: (Obscrve an employee from a small company}

a. Find P(B).

b. Find P(A fl B).

c. Find P(AUB).

d. Find P(A~B).

e. Are A and B independent? Justify your answer.