A survey of university students in Canada reported the following percentages. $30.0%40.0%30.0%100%\begin{array} { | l | l | l | l | l | } \hline & \text { Cat lover } & \text { Dog lover } & \text { Other } & \text { Total } \\\hline \text { Brand 1 Cola } & 22.5 \% & 28.0 \% & 16.5 \% & 67.0 \% \\\hline \text { Brand 2 Cola } & 7.5 \% & 12.0 \% & 13.5 \% & 33.0 \% \\\hline \text { Total } & 30.0 \% & 40.0 \% & 30.0 \% & 100 \% \\\hline\end{array}$ Find the conditional distribution of pet preference for students that prefer Brand 1 Cola.

A) 30.0% cat,40.0% dog,30.0% other
B) 22.5% cat,28.0% dog,16.5% other
C) 33.6% cat,41.8% dog,24.6% other
D) 22.7% cat,36.4% dog,40.9% other
E) 19.0% cat,24.0% dog,57.0% other

Question

A survey of university students in Canada reported the following percentages.

30.0%40.0%30.0%100%\begin{array} { | l | l | l | l | l | } \hline & \text { Cat lover } & \text { Dog lover } & \text { Other } & \text { Total } \\\hline \text { Brand 1 Cola } & 22.5 \% & 28.0 \% & 16.5 \% & 67.0 \% \\\hline \text { Brand 2 Cola } & 7.5 \% & 12.0 \% & 13.5 \% & 33.0 \% \\\hline \text { Total } & 30.0 \% & 40.0 \% & 30.0 \% & 100 \% \\\hline\end{array}

Find the conditional distribution of pet preference for students that prefer Brand 1 Cola.

A) 30.0% cat,40.0% dog,30.0% other
B) 22.5% cat,28.0% dog,16.5% other
C) 33.6% cat,41.8% dog,24.6% other
D) 22.7% cat,36.4% dog,40.9% other
E) 19.0% cat,24.0% dog,57.0% other

Peter Wenas · Accepted Answer

Final Answer : C, Explanation :   To find the conditional distribution of pet preference for students that prefer Brand 1 Cola, we divide the percentage of each pet preference within Brand 1 Cola by the total percentage of students who prefer Brand 1 Cola (67.0%). Thus, for cat lovers:   22.5 % / 67.0 % = 33.6 % 22.5\% / 67.0\% = 33.6\% 22.5%/67.0% = 33.6%  , for dog lovers:   28.0 % / 67.0 % = 41.8 % 28.0\% / 67.0\% = 41.8\% 28.0%/67.0% = 41.8%  , and for other:   16.5 % / 67.0 % = 24.6 % 16.5\% / 67.0\% = 24.6\% 16.5%/67.0% = 24.6%  .

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