Estimate the number of red fishes in the pond

[kudesnik]

hi all!

I have the following problem (in reality I study objects which may be perfectly described by "fishes" as below):

Fishes in the pond: There are N fishes (x of blue color and y of red color) in the pond. N>>10^5, x+y=N, x>>y Each fish has a weight w - positive numerical value. Suppose that the fishing process is a random selection among all the fishes (the probability for catching of blue fish is x/N, for red - y/N).
My tasks:
1) Given minimizing the number of catched fishes estimate the number of red fishes in the pond with predefined accuracy (5-15% would be just ok).
2) Given minimizing the number of catched fishes estimate the total weight of all red fishes.

I would appreciate any reference (I believe it certainly exists since the problem looks like very typical!) to a textbook or a web page in which this or similar problem is considered.

 

[HallsofIvy]

When you say "Given minimizing the number of catched fishes" do you mean that you are given some specific number of red and blue fish caught? without that information, I don't see how you can do this.

Edited after a little more thought- Clearly if you catch r red fish and b blue fish, with r+b= n, then the percentage of red fish in your catch is r/n. Given that the best estimate of the number of red fish in the entire lake is (r/n)N. You are asking for the smallest n such that you can still be sure that the estimate is within, say 15% of the true value.

Now, that I am clearer on what you are asking, I have to admit that I don't know enough statistics to answer that!