The table below shows the soft drinks preferences of people in three age groups. $$\begin{array} { l c c c }
& \text { Cola } & \text { Root Beer } & \text { Lemon-lime } \
\text { Under 21 years of age } & 40 & 25 & 20 \
\text { Between 21 and 40 } & 35 & 20 & 30 \
\text { Over 40 years of age } & 20 & 30 & 35
\end{array}$$ If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40.
A) $\frac { 2 } { 5 }$
B) $\frac { 2 } { 17 }$
C) $\frac { 6 } { 17 }$
D) None are correct

Question

The table below shows the soft drinks preferences of people in three age groups. $$\begin{array} { l c c c } 
& \text { Cola } & \text { Root Beer } & \text { Lemon-lime } \
\text { Under 21 years of age } & 40 & 25 & 20 \
\text { Between 21 and 40 } & 35 & 20 & 30 \
\text { Over 40 years of age } & 20 & 30 & 35
\end{array}$$ If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40. 
A) $\frac { 2 } { 5 }$
B) $\frac { 2 } { 17 }$
C) $\frac { 6 } { 17 }$
D) None are correct

Quizplus · Accepted Answer

The probability of someone being over 40 is $\frac{20+30+35}{255}=\frac{85}{255}=\frac{1}{3}$. Out of the people over 40, the probability of them drinking root beer is $\frac{30}{85}=\frac{6}{17}$, so the probability of someone being over 40 and drinking root beer is $\frac{1}{3}\cdot\frac{6}{17}=\frac{2}{17}$. Therefore, the probability that a randomly selected person drinks root beer given that they are over 40 is $\frac{30}{85}=\boxed{	extbf{(C) }\frac{6}{17}}.$

The Table Below Shows the Soft Drinks Preferences of People