1. Scientists in Amazon jungle want to find the best estimate for the African lion population. They tagged and released 20 African lion as part of a research project. Later, they found 160 African lion, 8 of which were tagged? Find the best estimate of population?

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1. Let the total population of African lions be $$ N $$.

2. In the first step, scientists tagged and released 20 lions.

3. Later, a sample of 160 lions was observed, and 8 of them were found to be tagged.

4. Using the capture-recapture method, we assume that the proportion of tagged lions in the sample is approximately equal to the proportion of tagged lions in the whole population. This gives us the equation:
   $$
   \frac{\text{Number of tagged lions in the population}}{N} \approx \frac{\text{Number of tagged lions in sample}}{\text{Total lions in sample}}.
   $$
   Plugging in the values:
   $$
   \frac{20}{N} \approx \frac{8}{160}.
   $$

5. Simplify the right-hand side:
   $$
   \frac{8}{160} = \frac{1}{20}.
   $$

6. Now we have:
   $$
   \frac{20}{N} = \frac{1}{20}.
   $$

7. Solve for $$ N $$ by cross-multiplying:
   $$
   20 \times 20 = N.
   $$
   $$
   N = 400.
   $$

8. Therefore, the best estimate of the African lion population is $$ 400 $$.
The best estimate of the African lion population is 400.

Scientists in Amazon jungle want to find the best estimate
for the African lion population. They tagged and released 20
African lion as part of a research project. Later, they found
160 African lion, 8 of which were tagged? Find the best
estimate of population?

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