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a. What is the probability of this later event if the lake contains n fish?

b. How can such data be used to estimate the number of fish remaining in the lake?

So suppose an isolated area has n creatures that we want to investigate.

She marked 50 fishes. Later she caught 50 and found 10 are tagged.

The probability of this happening is

(50 chooses 10)(n-50 chooses 40)/(n chooses 50)

Let's called the above probability f(n).

Of course, if there were n - 1 fishes, then f(n - 1) < f(n).

Using the inequality f(n - 1) < f(n), we should be able to solve for n.

Am I correct?

Thanks