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It is allowable to assume that the fish had time to evenly mix with the general population.

Since you caught 10% of the fish had tags (3/30), it makes sense that you caught 10% of the fish in the lake. If 40 is 10% of the population, the whole lake likely has around 400 fish.

check it. If there are 400 fish and 30 have tags, it makes sense that if you catch 40, 3 will have tags. ■

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Q: Suppose 30 fish are caught tagged and released into a lake Two weeks later 40 fish are caught of which 3 are found to have tags How would you estimate the number of fish in the lake?
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