Question

Biologists want to know how many fish are in a certain lake. On January 1, they removed 730 fish from the lake and tagged them. On February 1, they returned to the lake and collected a random sample of 380 fish, of which 40 had been previously tagged. How many fish does the lake have, based on this experiment?

Answer 1

Intuitive way: by proportion
Let x=population size.
then
x/730 = 380/40
solve for
x=(380/40)*730
=6935

Can also be solved using a hypergeometric distribution using a maximum likelihood estimate. Gives identical result in this case.