To estimate the number of fish in the lake, we can use the mark and recapture method. This method is commonly used in ecology to estimate population sizes of animals.
According to the given information, there are two sampling events:
1. The first event involves catching, tagging, and releasing 80 fish.
2. The second event involves catching 120 fish, out of which 3 are found to have tags.
Here's how we can solve this problem:
1. in the first sampling event, we catch and tag 80 fish.
2. In the second sampling event, we catch 120 fish, out of which 3 have tags. This tells us that the ratio of tagged fish in the second event to the total population is equal to the ratio of tagged fish in the first event to the total population.
3. Using this ratio, we can set up a proportion to estimate the total number of fish in the lake.
Let's denote the unknown total population of fish in the lake as 'x':
(tagged fish in second event / total fish in second event) = (tagged fish in first event / total fish in lake)
3/120 = 80/x
Cross multiplying, we get:
3x = 80 * 120
Simplifying:
3x = 9600
Dividing both sides by 3:
x = 3200
Hence, the estimated number of fish in the lake is 3200.
Therefore, the correct answer is option A. 3200.