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To estimate the number of fish in a lake, scientists use a tagging and recapturing technique. A number of fish are captured, tagged, and then released back into the lake. After a while, some fish are captured and the number of tagged fish is counted.
Let T be the total number of fish captured, tagged, and released into the lake, n the number of fish in a recaptured sample, and t the number of fish found tagged in that sample. Finally, let x be the number of fish in the lake. The assumption is that the ratio between tagged fish and the total number of fish in any sample is approximately the same, and hence scientists assume
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