So here we have an example problem that says, you and a group of population ecologists have been tasked with finding the population size of prairie dogs in a plot of land in Texas. You and your team captured 31 prairie dogs and marked them before releasing them back where you found them. 1 week later, you return to the same area and capture 47 prairie dogs, and 12 of them were already marked by your team the previous week. Estimate the total population of prairie dogs in the area. And we've got these 4 potential answer options down below.
Now, of course, this problem is related to the mark and recapture method. So recall from our last lesson video, the equation for that method is right here where mn is equal to rc. And so, recall that m is equal to the number of marked individuals in the first capture, which we're told there are 31 of them, so m is equal to 31. And that's going to be over n, which is the unknown total population size, so we'll leave that as the variable n. And this is going to be equal to r, which is the number of marked individuals in the second capture, and we're told in the problem that there are 12 of them, so r is equal to 12, and this is going to be over c, which is the total size of the second capture, which the problem tells us that there are 47 of them.
And so all we need to do is use our algebra skills to solve for the missing variable n here, and we can do that in many ways, but what we're going to do is take the reciprocal of both sides of the equation. So what we'll get is n31 is equal to 4712. And then all we need to do is multiply both sides of the equation by 31, and what we end up getting is n is equal to 4712 times 31. And so if you take your calculator and do 47 divided by 12 and then multiply that answer by 31, what you'll get is an answer for n that is about 121.42, about. And so notice that this answer right here matches closest with answer option c, which says 121.
So the correct answer to this example problem is option c, and that concludes this problem. So I'll see you all in our next video.