Question

In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A month later, 200 bears were captured of which 36 were tagged. About how many grizzly bears are in the population?

Answer 1

Answer:

539

Step-by-step explanation:

Let the total population of  grizzly bears=x

In the first capture, 97 were tagged.

Therefore, ratio of the total population to the tagged=x:97

A month later, when 200 bears were captured, 36 were tagged.

Ratio of the sample to the tagged=200:36

Since a sample is representative of the population, the ratios are the same. We therefore have:

x:97=200:36

$\dfrac{x}{97} =\dfrac{200}{36}\\ Cross multiply\\36x=200 X 97\\x=200 X 97 \div 36\\x=538.9 \approx 539$

There are about 539 grizzly bears in the population