SOLUTION: To determine the number of fish in a lake, a park ranger catches 260 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 20 of them are

Question 569571: To determine the number of fish in a lake, a park ranger catches 260 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 20 of them are tagged. Estimate the number of fish in the lake.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The ratio of total fish to tagged fish in the sample caught at the end is .
If the fish had time to redistribute throughout the lake after being tagged, you would expect that ratio to be the same for the total of fish in the lake. If no one else has been doing anything with the fish, we expect that the total number of tagged fish in the whole lake is the 260 tagged at the beginning of the problem.
So, we can write the proportion:

and we can solve for the total
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The total number of fish can be estimated as
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