# The following table describes the student population in a large colleg

The following table describes the student population in a large college.
$\begin{array}{|c|c|} \hline Class&Male&Female \\ \hline Freshman (\%)&20&15 \\ \hline Sophomore (\%)&13&10\\ \hline Juior (\%)&10&10\\ \hline Senior (\%)&17&5\\ \hline \end{array}$
a) Find the probability that a randomly selected student is female. (Enter your probability as a fraction.)
b) Find the probability that a randomly selected student is a junior. (Enter your probability as a fraction.)
c) If the selected student is a junior, find the probability that the student is female. (Enter your probability as a fraction.)

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Step 1
There is total $$\displaystyle{\left({20}+{13}+{10}+{17}+{15}+{10}+{10}+{5}\right)}\%={100}\%$$ students
Among them $$\displaystyle{\left({15}+{10}+{10}+{5}\right)}\%={40}\%$$ is female.
So the probability of female student $$\displaystyle={\frac{{{40}\%}}{{{100}\%}}}={\frac{{{2}}}{{{5}}}}$$
Step 2
There are $$\displaystyle{\left({10}+{10}\right)}\%={20}\%$$ juniors.
So the probability of junior $$\displaystyle={\frac{{{20}\%}}{{{100}\%}}}={\frac{{{1}}}{{{5}}}}$$
Step 3
c) $$\displaystyle{\left({10}+{10}\right)}\%={20}\%$$ students are junior. Among them 10% is female.
So the required probability $$\displaystyle={\frac{{{10}\%}}{{{20}\%}}}={\frac{{{1}}}{{{2}}}}$$
Answer(a): $$\displaystyle{\frac{{{2}}}{{{5}}}}$$
Answer (b): $$\displaystyle{\frac{{{1}}}{{{5}}}}$$
Answer (c): $$\displaystyle{\frac{{{1}}}{{{2}}}}$$