You catch and tag 100 fish from a lake and release them unharmed. The next day you return and catch 100 fish again, but only 20 of them are tagged. Estimate the total number of fish in the lake.
Assume that in a day the 100 fish are distributed evenly throughout the population.
Since 20% of the 100 fish caught were tagged, you assume that 20% of the whole lake population are now tagged. So, if 100 tagged fish are 20%, there are 500 fish in the lake.
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In a wildlife preserve 45 elephants are caught, tagged, and released. Later 52 elephants are caught and 13 of them have tags. Approximately, how many elephants are there in the wildlife preserve?
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To estimate the total number of fish in the lake, we can use a method called the Lincoln-Petersen Index. This index assumes that the proportion of tagged fish in the first sample represents the proportion of tagged fish in the whole population.
Here's how you can use the Lincoln-Petersen Index to estimate the total number of fish in the lake:
1. Let's denote the total number of fish in the lake as "N."
2. The number of fish caught and tagged in the first sample is 100.
3. The number of fish caught in the second sample is also 100.
4. The number of tagged fish caught in the second sample is 20.
Now, we can use the Lincoln-Petersen Index formula:
N = (M2 * S) / T
Where:
- N is the estimated total number of fish in the lake
- M2 is the total number of fish caught in the second sample (100)
- S is the total number of fish caught and tagged in the first sample (100)
- T is the number of tagged fish caught in the second sample (20)
Substituting the values into the formula:
N = (100 * 100) / 20
N = 500
Therefore, the estimated total number of fish in the lake is 500.