A large corporation has spent considerable time developing em$-$

ployee performance rating scales to evaluate an employee$$s job performance

on a regular basis, so major adjustments can be made when needed and em$-$

ployees 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 $0\mathrm{.}010\mathrm{.}020\mathrm{.}020\mathrm{.}04$

Medium $0\mathrm{.}050\mathrm{.}060\mathrm{.}070\mathrm{.}10$

High $0\mathrm{.}100\mathrm{.}150\mathrm{.}160\mathrm{.}22$

The probabilities for being placed on a 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$).(3$ points$)$

$($b$)$ Find P $($B$).(3$ points$)$

$1$