The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Age at Retirement $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Career } & 50 - 55 & 56 - 60 & 61 - 65 & \text { Over 65 } & \text { Total } \
\hline \text { Attorney } & 11 & 46 & 97 & 39 & 193 \
\hline \begin{array} { c }
\text { College } \
\text { Professor }
\end{array} & 9 & 37 & 90 & 48 & 184 \
\hline \text { Secretary } & 21 & 45 & 63 & 49 & 178 \
\hline \text { Store Clerk } & 18 & 44 & 70 & 50 & 182 \
\hline \text { Total } & 59 & 172 & 320 & 186 & 737 \
\hline
\end{array}$$ Find the probability that the person was a secretary or retired before the age of 61.
A)0.465
B)0.286
C)0.090
D)0.555
E)0.414

Question

The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. Age at Retirement $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Career } & 50 - 55 & 56 - 60 & 61 - 65 & \text { Over 65 } & \text { Total } \
\hline \text { Attorney } & 11 & 46 & 97 & 39 & 193 \
\hline \begin{array} { c } 
\text { College } \
\text { Professor }
\end{array} & 9 & 37 & 90 & 48 & 184 \
\hline \text { Secretary } & 21 & 45 & 63 & 49 & 178 \
\hline \text { Store Clerk } & 18 & 44 & 70 & 50 & 182 \
\hline \text { Total } & 59 & 172 & 320 & 186 & 737 \
\hline
\end{array}$$ Find the probability that the person was a secretary or retired before the age of 61.
A)0.465
B)0.286
C)0.090
D)0.555
E)0.414

Quizplus · Accepted Answer

The probability that the person was a secretary is 178/737 = 0.242. The probability that the person retired before the age of 61 is (59+172)/737 = 0.311. The probability that the person was a secretary or retired before the age of 61 is 0.242 + 0.311 - 0.058 = 0.495.

The Following Contingency Table Provides a Joint Frequency Distribution for a Group