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?

Question

Allison · Answer

Sooooo this question is screwing with my low IQ points and if I think about it any more, I'll have no IQ points. Do you still need help? XD

sillybilly123 · Answer

If the fish pop on T = Jan 1 is N, and they tagged 730, so we say probability of being tagged is $P(T) = \frac{730}{N}$

Regardless of the fish pop, N',  on T' = Feb 1,  we can say that prob of being tagged then is $P(T') = \frac{40}{380}$, coz that is what the experiment revealed.

But we can also say that $P(T') = \frac{730}{N'}$, based on certain assumptions, such as none of the originally-tagged fish having died.

It follows from this "logic" that:

$ P(T') = \frac{40}{380} = \frac{730}{N'} \implies N' = 6935$