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

Guest Oct 19, 2016

#2**+10 **

**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**

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

heureka
Oct 19, 2016

#1**+10 **

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.

geno3141
Oct 19, 2016

#2**+10 **

Best Answer

**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**

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

heureka
Oct 19, 2016

#3**+5 **

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!

Melody
Oct 19, 2016