The following table describes the student population in a large colleg

Coroware 2021-11-20 Answered
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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Expert Answer

Fommeirj
Answered 2021-11-21 Author has 6410 answers
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): \(\displaystyle{\frac{{{1}}}{{{2}}}}\)
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