Question: A large corporation has spent considerable time developing employee performance rating scales to evaluate an employee’s job performance on a regular basis, so major adjustments can be made when needed and employees who should be considered for a “fast track” can be isolated. Keys to this latter determination are ratings on the ability of an employee to perform to his or her capabilities and on his or her formal training for the job.

FORMAL TRAINING

WORKLOAD CAPACITY NONE LITTLE SOME EXTENSIVE

Low .01 .02 .02 .04

Medium .05 .06 .07 .10

High .10 .15 .16 .22

The probabilities for being places on the fast track are as indicated for the 12 categories of workload capacity and formal training. The following three events (A,B, and C) are defined:

A: an employee works at the high capacity level

B. An employee falls into the highest (extensive) formal training category

C. an employee has little or no formal training and works below high capacity

a. Find P(A), P(B), and P(C)

b. Find P(A|B), P(A| \(\bar{B}\) ), and P( \(\bar{B}\) |C)

c. Find P(A U B), P(A ∩C) and P(B∩ C)