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

539

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

`(x)/(97) =(200)/(36)\\ $Cross multiply\\36x=200 X 97\\x=200 X 97 / 36\\x=538.9 \approx 539`

There are about 539 grizzly bears in the population