To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population?

If 2 out of 100 bears have the tags and there are 50 tags total, then the total number of bears is 25 times larger than the second sample (50/2 = 25).  This is equivalent to asking how many bears must be located if all 50 of the original tags are to be found.  You must locate 25 groups of 100 bears, each group having 2 tags, to find all 50 tags.  Which is 2500 bears.

The total number of bears is approximately 100 x 25 = 2500 bears.

Note that this is a statistical estimate and NOT the true number of bears.