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6
6
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1990 AIME Problems
Problems
(1)
Count the Fish!
Source:
2/24/2006
A biologist wants to calculate the number of fish in a lake. On May 1 she catches a random sample of 60 fish, tags them, and releases them. On September 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. To calculate the number of fish in the lake on May 1, she assumes that
25
%
25\%
25%
of these fish are no longer in the lake on September 1 (because of death and emigrations), that
40
%
40\%
40%
of the fish were not in the lake May 1 (because of births and immigrations), and that the number of untagged fish and tagged fish in the September 1 sample are representative of the total population. What does the biologist calculate for the number of fish in the lake on May 1?
ratio
AMC
AIME
percent