Algebra

Quote:

Originally Posted by sureshrju

game warden use experiments to helpdetermine the number of fish in a lake. suppose 180 fish are caught, tagged, and released. two weeks later, 80 fish are caught, 6 of which are found to have tags. using this information, estimate the number of fish in the lake.

The 6 tagged fish among the 80 caught reflects the proportion of tagged fish to the lake population.

For instance, we'd expect about 3 in 40 to be tagged, or 12 in 160 based on that.

Hence the ratios $\frac{6}{80}\ and\ \frac{180}{total}$ ought be approximately equal.

By catching a number of fish initially and tagging them,
a certain proportion or percentage of tagged fish to the entire fish population of the lake has been established.

Then, the number of fish caught that have tags afterwards should about reflect that proportion.

The group ratio ought to approximately reflect the population ratio "on average".