Problem:
A biologist wants to calculate the number of fish in a lake. On May she catches a random sample of fish, tags them, and releases them. On September she catches a random sample of fish and finds that of them are tagged. To calculate the number of fish in the lake on May , she assumes that of these fish are no longer in the lake on September (because of death and emigrations), that of the fish present on September were not in the lake on May (because of births and immigrations) and that the numbers of untagged fish and tagged fish in the September sample are representative of the total population. What does the biologist calculate for the number of fish in the lake on May
Solution:
Let
From the data in the problem we find that , and that the number of tagged fish in the lake on September is . Thus, assuming the tagged fish are fairly represented in the September sample, we have
Hence and .
The problems on this page are the property of the MAA's American Mathematics Competitions