Use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event.
-The person has normal cholesterol or is 61 or older. $\begin{array}{|l|c|c|c|}
\hline & \begin{array}{c}
\text { Normal } \
\text { Cholesterol }
\end{array} & \begin{array}{c}
\text { Elevated } \
\text { Cholesterol }
\end{array} & \text { Total } \
\hline \begin{array}{l}
\mathbf{3 0} \text { and } \
\text { under }
\end{array} & 11 & 5 & 16 \
\hline \text { 31-60 } & 45 & 31 & 76 \
\hline \text { 61 or older } & 18 & 90 & 108 \
\hline \text { Total } & 74 & 126 & 200 \
\hline
\end{array}$
A) $\frac { 41 } { 50 }$
B) $\frac { 91 } { 100 }$
C) $\frac { 9 } { 50 }$
D) $\frac { 37 } { 100 }$

Question

Quizplus · Accepted Answer

The probability of selecting someone with normal cholesterol or 61 or older is the sum of the probabilities of each individual event, minus the overlap (since people 61 or older with normal cholesterol are counted in both categories). There are 74 people with normal cholesterol and 108 people who are 61 or older. However, 18 of those 61 or older have normal cholesterol, which we've already counted in the 74. So, we don't subtract anything because we're looking for the union of both events, not the intersection. Therefore, the total number of people who have normal cholesterol or are 61 or older is 74 (normal cholesterol) + 90 (61 or older with elevated cholesterol) = 164. The total number of people in the study is 200. Thus, the probability is $ \frac{164}{200} = \frac{41}{50} $.

Use the Data in the Table Categorizing Cholesterol Levels by the Ages