Statistics

college class contains 62 students,

of these 32 are freshman,

32 are economics major,

and 12 are neither.

what is the probablity the student is both a freshman and economics major

\(\begin{array}{|lcll|} \hline \text{Set students } ~ s &=& 62 \\ \text{Set freshman } ~ f &=& 32 \\ \text{Set economics major} ~ e_m &=& 32 \\ \text{Set neither} ~ n &=& 12 \\\\ \text{both a freshman and economics major } &=& f+e_m+n -s \\ &=& 32+32+12-62 \\ &=& 14 \\\\ \text{the probablity is the student is both a freshman and economics major } &=& \frac{f+e_m+n -s}{s} \\ &=& \frac{14}{62} \\ &=& \frac{7}{31} \quad ( 22.58\ \%)\\ \hline \end{array} \)

Of  62  students,  32  are freshmen,  32  are economic majors, and  12  are neither.

Subtract  12  from  62, giving  50  students who are either freshmen, economic majors or both.

If being a freshman is independent from being an economic major, adding the number of fresmen to the number of economic majors could, at most, be  50  students.

However, when you add  32  freshmen to the  32  economic majors, you get a total of  64 students. This means that   14  students must be both freshmen and economic majors (you get  14 by subtracting  50  from  64).

The probability that a student, drawn at random, is both an economics major and a freshman is:

14 /  62  =  7/31.

That is an interesting way to use an array.  Thanks Heureka.

I stored it away in our LaTex thread fir reference.

I meant it to be shown as code and then displayed afterwards but for some strange reason even the code that was not included in the LaTex box has displayed as if it was.  Weird....    More forum gremlins!     

http://web2.0calc.com/questions/latex#r85