Question

1. the managers of a corporation were surveyed to determine the background that leads to a successful manager. each manager was rated as being either a good, fair, or poor manager by his/her boss. the manager’s educational background was also noted. the data appear below.

educational background

manager rating	h. s. degree	some college	college degree	master’s or ph.d
fair	8	16	45	18
poor	9	4	6	15

(6pts) given that a manager is a good manager, what is the probability that this manager has some college background?

Explanation:

Step1: Calculate total number of good managers

Add up the number of good managers across all educational - backgrounds.
$5 + 1+28 + 5=39$

Step2: Determine number of good managers with some college background

The number of good managers with some college background is 1.

Step3: Calculate the conditional probability

Use the formula for conditional probability $P(A|B)=\frac{n(A\cap B)}{n(B)}$. Here, event $A$ is having some college background and event $B$ is being a good manager. So the probability is $\frac{1}{39}$.

Answer:

$\frac{1}{39}$