Example 3.5.14

Tagging fish is a means of estimating the size of the population of fish in a body of water (such as a lake). A sample of fish is taken, tagged, and then redistributed into the lake. When another sample is taken, the proportion of fish that are tagged out of that sample are assumed to be proportional to the total number of fish tagged out of the entire population of fish in the lake.

\begin{equation*} \frac{\text{number of tagged fish in sample}}{\text{number of fish in sample}}=\frac{\text{number of tagged fish total}}{\text{number of fish total}} \end{equation*}

Assume that \(90\) fish are caught and tagged. Once they are redistributed, a sample of \(200\) fish is taken. Of these, \(7\) are tagged. Estimate how many fish total are in the lake.