+118658 +118658 This little gem is Heureka's - thanks Heureka :)
http://web2.0calc.com/questions/statistics_427#r2
\begin{array}{|lcll|} \hline \text{Set students } ~ s &=& 62 \\ \text{Set freshman } ~ f &=& 32 \\ \text{Set economics major} ~ e_m &=& 32 \\ \text{Set neither} ~ n &=& 12 \\\\ \text{both a freshman and economics major } &=& f+e_m+n -s \\ &=& 32+32+12-62 \\ &=& 14 \\\\ \text{the probablity is the student is both a freshman and economics major } &=& \frac{f+e_m+n -s}{s} \\ &=& \frac{14}{62} \\ &=& \frac{7}{31} \quad ( 22.58\ \%)\\ \hline \end{array}
\(\begin{array}{|lcll|} \hline \text{Set students } ~ s &=& 62 \\ \text{Set freshman } ~ f &=& 32 \\ \text{Set economics major} ~ e_m &=& 32 \\ \text{Set neither} ~ n &=& 12 \\\\ \text{both a freshman and economics major } &=& f+e_m+n -s \\ &=& 32+32+12-62 \\ &=& 14 \\\\ \text{the probablity is the student is both a freshman and economics major } &=& \frac{f+e_m+n -s}{s} \\ &=& \frac{14}{62} \\ &=& \frac{7}{31} \quad ( 22.58\ \%)\\ \hline \end{array}\)
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