Question

An employee is classified in one of three categories of performance: outstanding, satisfactory, or unsatisfactory. Each employee is either probationary or appointive. Human resources determines that 60% of employees are probationary. Further, it is known that 3% are satisfactory. 10% are outstanding and probationary, while 1% are appointive and unsatisfactory.

a. Using a contingency table, show how every employee in the company is categorized according to this system.

b. Denote outstanding, satisfactory and unsatisfactory by O, S, and U, and denote probationary and appointive as P and A. Find ?(? ∩ ?) and explain the meaning of your answer.

c. Find ?(?|?) and explain the meaning of your answer.

d. Find ?(?|?) and explain the meaning of your answer.

e. Find ?(?|?) and explain the meaning of your answer.

f. Anyone who is outstanding or satisfactory is deemed to be a worthy employee of the company. According to the data in this problem, who has a higher rate of “worthiness”, those who are probationary or those who are appointive? Use probability computations to justify your reasoning.

g. If I were to tell you that I talked to a satisfactory employee today, what kind of employee am I most likely talking about? Explain

E F and G only please

Answer 1