Abiologist caught and tagged 250 fish. when she collected a sample of 75 fish, 5 of them were tagged. how many fish would she estimate are in the lake?

We can estimate the number of fish in the lake by doing a simple proportion from the sample size the biologist collected.

Since the biologist has tagged 5 out of the 75 she collected, we can estimate that the same ratio can be generalized for the entire population of fish in the lake.

We then arrive with the following proportion:

where x is the number of fish in the lake.

Solving the proportion we arrive at the final answer of 3,750 fish in the lake.