To determine the number of deer in a game preserve, a conservationist catches 810 deer, tags them and lets them loose. Later 684 deer are caught; 171 of them are caught. How many deer are in the preserve?
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To determine the number of deer in a game preserve, a conservationist catches 810 deer, tags them and lets them loose. Later 684 deer are caught; 171 of them are tagged. How many deer are in the preserve?
To determine the number of deer in the preserve, we can use a technique called mark and recapture. This method involves catching a certain number of individuals, marking them, releasing them, and then recapturing a second sample later on. By comparing the number of marked individuals recaptured in the second sample to the total number of individuals recaptured, we can estimate the total population size.
Let's break down the information given in the question:
- In the first round, the conservationist catches and tags 810 deer.
- In the second round, 684 deer are caught, and 171 of them are tagged.
To apply the mark and recapture method, we can set up a proportion:
(First round marked deer) / (Total population size) = (Second round marked deer) / (Second round total deer)
Plugging in the given values:
810 / (Total population size) = 171 / 684
Now we can solve for the total population size by cross-multiplying:
810 * 684 = 171 * (Total population size)
554,040 = 171 * (Total population size)
Dividing both sides by 171:
554,040 / 171 = Total population size
This gives us the estimated total population size of the deer in the preserve. Evaluating the expression:
Total population size ≈ 3,240
Therefore, there are approximately 3,240 deer in the game preserve.