We will investigate the fraction of non-fiction biography books in a library.
There are certain proportions that are given as follows:
[tex]p_{non-fiction}\text{ = }\frac{Number\text{ of non-fiction books}}{Total\text{ number of books}}\text{ = }\frac{2}{5}[/tex][tex]q_{biography\text{ }}=\text{ }\frac{Number\text{ of biography books}}{Number\text{ of non-fiction books}}\text{ = }\frac{1}{5}[/tex]To determine the number of non-fictional biography books we will develop a compound proportions that would leave to following fraction:
[tex]\frac{Number\text{ of non-fiction biography}}{Total\text{ number of books}}[/tex]We can write the above fraction as a compounding off two given fraction ( p and q ) as follows:
[tex]\begin{gathered} \frac{\text{non-fiction biography books}}{\text{Total number of books}}=p_{non-fiction}\cdot q_{biography} \\ \\ \frac{\text{non-fiction biography books}}{\text{Total number of books}}=\frac{2}{5}\cdot\frac{1}{5} \\ \\ \frac{\text{non-fiction biography books}}{\text{Total number of books}}=\frac{2}{25} \end{gathered}[/tex]Therefore, the fraction of non-fiction biography is:
[tex]\frac{2}{25}[/tex]