The table below lists the results of a survey of a random sample of 400 high school students. Each student selected one subject that was his or her favorite.

$$ \text{Favorite High School Subjects} \\ $$ $$\footnotesize \begin{array} {|c|c|c|c|c|c|c|c|} \hline & \text{English} & \text{Art} & \text{Math} & \text{History} & \text{Science} & \text{Other} & \text{Total} \\ \hline \text{Freshmen} & 13 & 12 & 15 &18 & 25 & 17 & 100 \\ \hline \text{Sophomores} & 18 & 14 & 11 &22 & 15 & 20 & 100 \\ \hline \text{Juniors} & 5 & 10 & 23 & 13 & 31 & 18 & 100 \\ \hline \text{Seniors} & 23 & 5 & 33 & 13 & 12 & 14 & 100 \\ \hline \text{Total} & 59& 41&82 &66 &83 &69 & 400 \\ \hline \end{array} $$

If one of the students from the sample is selected at random, which of the following is closest to the probability that the student is a sophomore or junior who selected science or math as his or her favorite high school subject?

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We wish to find the following:

$$ \frac{\colorbox{aqua}{\text{Sophomore or junior who selected science or math}}}{\colorbox{yellow}{\text{A student from the sample}}} $$

Using the data from the table:

$$ \begin{array} {|c|c|c|c|c|c|c|c|} \hline & \text{English} & \text{Art} & \text{Math} & \text{History} & \text{Science} & \text{Other} & \text{Total} \\ \hline \text{Freshmen} & 13 & 12 & 15 &18 & 25 & 17 & 100 \\ \hline \text{Sophomores} & 18 & 14 & \colorbox{aqua}{$11$} &22 & \colorbox{aqua}{$15$} & 20 & 100 \\ \hline \text{Juniors} & 5 &10 & \colorbox{aqua}{$23$} & 13 & \colorbox{aqua}{$31$} & 18 & 100 \\ \hline \text{Seniors} & 23 & 5 & 33 & 13 & 12 & 14 & 100 \\ \hline \text{Total} & 59& 41&82 &66 &83 &69 & \colorbox{yellow}{$400$} \\ \hline \end{array} $$ $$ \frac{\colorbox{aqua}{\text{Sophomore or junior who selected science or math}}}{\colorbox{yellow}{\text{A student from the sample}}} $$ $$ =\frac{11+23+15+31}{400}$$ $$ = \frac{80}{400} $$ $$ = \boxed{0.20} $$