Real tricky rational question!!?

Question

To determine the number of deer in a game preserve,a conservationist catches 321 deer, tags them and lets them loose. Later 747 deer are caught 249 of them are tagged.

How many deer are in the preserve? ____deer

Answer 1

Alright, we're talking about fairly large numbers here, so rational techniques should be reasonably accurate. (Providing he caught them the right way.)

249 of the dear he caught are tagged, so we can assume that 249/747 of all the deer in the park are tagged. To get the total number of deer, we divide 321 by (249/747), which is (747*321/249)
I won't insult you're intelligence by doing the arithmatic for you.

Another good point would be to include an estimate of the reliability of the figure. I'd need to look up my old stats books to give you an accurate answer, but I'd guess there'd be about 2-3% error in those figures.

Answer 2

The idea is that if 249 out of 747 deer caught are tagged (249/747) that's some x percentage of tagged dear in your sample. You would expect that the total number of dear you tagged in the first place would have to be that x percent of the total number of deer out there.

We can solve this using a ratio.

249/747 = 321/y

In this ratio, we're asking how many total dear are there, y, that will make that ratio of tagged to total dear the same as our sample, 249/747

We can solve by cross multiplying:

249y = 747*321
y = (747*321)/249
y = 963

That's the total number of deep we would expect. I'm sure someone well versed in statistics could express the likelyhood that our answer was correct to any certain extent.

--charlie

Answer 3

Let N be the number of deer in the game preserve, of which n are tagged. n is known but N is unknown. If x be the number of the deer caught in a sample and out of them y are tagged, we can say that the ratio of N to x will be equal to the ratio of n to y.

N:x :: n:y

N = n . x / y = 321 . 747 / 249 = 963

This will be a fairly good estimate of the deer population.

Answer 4

Completely indeterminable! I mean just for starters when exactly is later? The deer could have had kiddies or anything! (Clearly you have too much time on your hand!)