10. the managers of a corporation were surveyed to determine the background that leads to a successful…

10. 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.\neducational background\n| manager rating | h. s. degree | some college | college degree | master’s or ph.d |\n| ---- | ---- | ---- | ---- | ---- |\n| good | 5 | 1 | 28 | 5 |\n| fair | 8 | 16 | 45 | 18 |\n| poor | 9 | 4 | 6 | 15 |\n(6pts) given that a manager is a good manager, what is the probability that this manager has some college background?

10. 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.\neducational background\n| manager rating | h. s. degree | some college | college degree | master’s or ph.d |\n| ---- | ---- | ---- | ---- | ---- |\n| good | 5 | 1 | 28 | 5 |\n| fair | 8 | 16 | 45 | 18 |\n| poor | 9 | 4 | 6 | 15 |\n(6pts) given that a manager is a good manager, what is the probability that this manager has some college background?

Answer

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:

$\frac{1}{39}$