To determine the number of deer in a game preserve, a conservationist catches 874 deer, tags them and lets them loos. Later, 708 deer are caught, 177 of them are tagged, how many deer are in the preserve?

Thank you in advance.

177/708 or 25% of the deer caught in the second round were tagged.

Which implies that the conservationist must have tagged 25% of the deer population in the preserve.
So the original 874 deers must represent 25% of the deer population.

.25x = 874
x = 874/.25 = 3496

So there must have been approximately 3500 deer.

To determine the number of deer in the preserve, we can use a method called mark and recapture. This involves tagging a sample of deer, releasing them back into the preserve, and then capturing another sample later to see how many of them are tagged.

Let's break down the information given:
- Initially, 874 deer are caught and tagged.
- Later, another sample of deer is captured, totaling 708 individuals.
- Out of the 708 captured deer, 177 of them are tagged.

To solve for the total number of deer in the preserve, we can set up a proportion using the mark and recapture method:

(Tagged Deer in Initial Sample) / (Total Number of Deer in Preserve) = (Tagged Deer in Later Sample) / (Total Number of Deer in Later Sample)

Let's plug in the given information:
(874) / (Total Number of Deer in Preserve) = (177) / (708)

Now, we can cross-multiply and solve for the total number of deer in the preserve:
874 * 708 = 177 * (Total Number of Deer in Preserve)
618,192 = 177 * (Total Number of Deer in Preserve)

To isolate the variable, divide both sides of the equation by 177:
618,192 / 177 = Total Number of Deer in Preserve

Therefore, the total number of deer in the preserve is approximately 3,492.

Remember, mark and recapture is an estimation method, and the accuracy of the estimate relies on several assumptions, such as the population remaining constant and the random mixing of tagged and untagged individuals.