Game wardens use experiments to help determine the number of fish in a lake. Suppose 80 fish are caught, tagged, and released back into the lake. Two weeks later, 120 fish are caught, three of which are found to have tags. Using this information, estimate the number of fish in the lake.
A. 3200.
B. 600.
C. 120.
D. 280.
We can use a proportion to estimate the number of fish in the lake. Let x be the total number of fish in the lake. We can set up the proportion:
80/x = 3/120
Simplifying this proportion, we get:
80/x = 1/40
Multiplying both sides by x, we get:
80 = x/40
Multiplying both sides by 40, we get:
x = 3200
Therefore, the estimated number of fish in the lake is 3200. The answer is A.
To estimate the number of fish in the lake, we can use a method called the mark and recapture technique.
Step 1: Calculate the proportion of tagged fish in the second sample.
The proportion of tagged fish in the second sample is found by dividing the number of tagged fish in the second sample (3) by the total number of fish caught in the second sample (120).
Proportion of tagged fish = 3 / 120 = 0.025
Step 2: Estimate the total fish population.
The total fish population can be estimated using the formula:
Total fish population = (Total number of tagged fish in the first sample * Total number of fish in the second sample) / Number of tagged fish recaptured in the second sample
Total fish population = (80 * 120) / 3
Calculating this, we get:
Total fish population = (9600) / 3
Total fish population ≈ 3200
Therefore, the estimated number of fish in the lake is approximately 3200.
The correct answer is A. 3200.
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.