$$ \begin{array} {|c|} \hline \text{Participates in} \\ \text{athletic program} \\ \hline \text{Yes} \\ \hline \text{No} \\ \hline \end{array} \begin{array} { c c |} \hline \text{Type of college} \\ \hline \text{2-year} & \text{4-year} \\ \hline 43 & 37 \\ \hline 45& 25 \\ \hline \end{array} $$

The table above summarizes the results of a survey in which 150 physical education majors were asked whether they attend a 2- or 4-year college program and whether they participate in a college athletic program. If one of the 150 students is selected at random, what is the probability that the student selected would be attending a 2-year college program and participating in a college athletic program?

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We are asked to find the probability of a student who is attending a 2-year college program and is participating in an athletic program.

$$ \begin{array} {|c|} \hline \text{Participates in} \\ \text{athletic program} \\ \hline \colorbox{yellow}{Yes} \\ \hline \text{No} \\ \hline \end{array} \begin{array} { c c |} \hline \text{Type of college} \\ \hline \colorbox{yellow}{2-year} & \text{4-year} \\ \hline \colorbox{aqua}{$43$} & 37 \\ \hline 45& 25 \\ \hline \end{array} $$ $$ \frac{\text{2-year college and participating in athletic program}}{\text{random student}} $$ $$ = \frac{43}{150} $$ $$ \approx \boxed{0.287} $$