Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The managerʹs educational background was also noted. The data appear below:
$\begin{array}{l}
\text { Educational Background }\
\begin{array} { l | c c c c | c }
\text { Manager } & & & & & \
\text { Rating } & \text { H. S. Degree } & \text { Some College } & \text { College Degree } & \text { Master's or Ph.D. } & \text { Total } \
\hline \text { Good } & 1 & 2 & 21 & 15 & 39 \
\text { Fair } & 3 & 19 & 43 & 22 & 87 \
\text { Poor } & 7 & 6 & 8 & 13 & 34 \
\hline \text { Total } & 11 & 27 & 72 & 50 & 160
\end{array}
\end{array}$
What is the probability that a randomly chosen manager has earned at least one college degree?

Question

Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The managerʹs educational background was also noted. The data appear below: 
$\begin{array}{l}
\text { Educational Background }\
\begin{array} { l | c c c c | c } 
\text { Manager } & & & & & \
\text { Rating } & \text { H. S. Degree } & \text { Some College } & \text { College Degree } & \text { Master's or Ph.D. } & \text { Total } \
\hline \text { Good } & 1 & 2 & 21 & 15 & 39 \
\text { Fair } & 3 & 19 & 43 & 22 & 87 \
\text { Poor } & 7 & 6 & 8 & 13 & 34 \
\hline \text { Total } & 11 & 27 & 72 & 50 & 160
\end{array}
\end{array}$
What is the probability that a randomly chosen manager has earned at least one college degree?

Quizplus · Accepted Answer

The probability that a randomly chosen manager has earned at least one college degree is calculated by adding the number of managers with a College Degree and those with a Master's or Ph.D., then dividing by the total number of managers. This gives $\frac{72 + 50}{160} = \frac{122}{160} = \frac{61}{80}$.

Each Manager of a Fortune 500 Company Was Rated as Being