Estimate the number of elk in the nature preserve.

Question

In a nature preserve 126 elk are caught and tagged. Later 75 elk are caught in the same preserve and 45 are found to have tags. Estimate the number of elk in the nature preserve.

Answer 1

As we only know about these two events, and are left to assume that no elk were tagged during the second event, we must make our best estimate using the information given.

 

First, notice the ratio in event two of tagged elk - 45:75. If we were to continue collecting samples of elk for a certain period of time, and continued tagging the untagged elk, we might expect a similar ratio at first & an ever increasing ratio aftwrward - at least until all the elk are someday tagged. We don't have any of that data, so we are obliged to use only this to extrapolate an estimate. It's okay - estimates are not really accurate, so the answer is less important than the process you use.

 

Second, can you apply the 45:75 ratio to the original number of tagged elk? Try reducing this ratio to smaller terms: both 45 & 75 are divisible by 15, so what happens when we do that division? The ratio becomes 3:5. This should be easier to apply to the original count, 126.

 

Finally, if 3 of every 5 elk are tagged, how do we manipulate 126 to arrive at our estimate? 126 represents tagged elk, so it is the "3" part - but how does the 5 come in? Think of it this way, 2:5 of the total elk are running around the preserve untagged. Let's divide 126 by 3. This gives us a number (42) that is 1/5 of the total number of elk, which we then multiply by 5. Another approach would be to multiply 42 by 2, then add the result to 126.

 

Remember, this estimate is probably not very accurate, but the process is correct - based upon the information available.