In a large forest, 300 deer were caught, tagged, and returned during 2001. During 2002, 500 deer were caught at random, of which only 20 had tags from the previous year. If the percent of deer in the forest that had tags during the second year and were caught in the 500 deer sample is representative of the percent of the total deer population in the forest with tags, what is the total deer population in the forest (assuming no change in population between 2001 and 2002)?
Correct answer: E
Explanation
Let N = the total number of deer in the forest.
During the first year, the percent of deer in the entire population with tags was: 300/N
20/500 is the percent of deer caught during the second year that had tags. Since this sample percent matches the percent for the entire population (i.e., the total number of tagged deer divided by the total number of deer), the two ratios are equal.
Equating these two percents:
Sample = Population
(20/500)=(300/N)
N = (300/1)*(500/20)
N=7500
Answer E
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