As part of a conservation effort for a lake, 70 fish were caught, tagged, and then released. Later, 80 fish were caught from the lake. Four of these 80 fish were found to have tags. Estimate the number of fish in the lake.
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To estimate the number of fish in the lake, we can use a method called the mark and recapture technique. This method assumes that the proportion of tagged fish in the second sample is representative of the proportion of tagged fish in the entire population.
Here's how we can calculate the estimated population size:
1. Catch, Tag, and Release: In the initial catch, 70 fish were caught and tagged. Let's call this "n1."
2. Second Catch: Later, 80 fish were caught from the lake, and among those, 4 had tags. Let's call this "n2" and "t."
3. Calculation: We can use the following formula to estimate the population size (N):
N = (n1 * n2) / t
4. Substitute the values:
N = (70 * 80) / 4
N ≈ 1400
Therefore, based on this estimation, there are approximately 1400 fish in the lake.