To determine the number of deer in a game preserve, a conservationist catches 428 deer, tags them and lets them loose. Later 644 deer are caught.161 of them are tagged. How many deer are in the preserve?
what is ...
Deernumber/644 = 428/161
886
To determine the number of deer in the game preserve, we can use a method called marking and recapture. This method involves catching a certain number of deer, marking them (tagging), releasing them back into the preserve, and then capturing a second sample of deer later on to see how many of them are marked.
In this case, the conservationist caught 428 deer and tagged them before releasing them back into the preserve. Later on, they captured a second sample of 644 deer, out of which 161 were tagged.
Now, to estimate the total number of deer in the preserve, we can set up a proportion based on the number of tagged deer in the second sample compared to the total number of deer in the preserve:
(Number of tagged deer in the first sample) / (Total number of deer in the preserve) = (Number of tagged deer in the second sample) / (Number of deer in the second sample)
Let's plug in the given values:
428 (tagged deer in the first sample) / (Total number of deer in the preserve) = 161 (tagged deer in the second sample) / 644 (total number of deer in the second sample)
To solve for the total number of deer in the preserve, we can cross-multiply and then solve for the unknown value:
428 * 644 = 161 * (Total number of deer in the preserve)
275,392 = 161 * (Total number of deer in the preserve)
Now, divide both sides of the equation by 161:
(Total number of deer in the preserve) = 275,392 / 161
Calculating this gives us:
(Total number of deer in the preserve) ≈ 1711
Therefore, according to the marking and recapture method, there are approximately 1,711 deer in the game preserve.