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It happens too rarely: stumbling across a method of clever simplicity.
Take the ecologist's way of estimating populations:
catch a sample and mark the specimens then release them.
After enough time for the sample to have mixed well with the
local population, take another sample, mark them differently
and note how many were marked in the previous sample.
The population estimate can be generated from just this data
- though follow on samples would usually be taken.
The estimated population is given by the first count times
second count divided by the number
re-caught of those marked first time.
Justification: it is reasonable to suppose that the number in
the second sample includes the number previously marked in a
similar ratio to the number in the entire population
compared with the number in the first count.....
Brian Whatcott Altus OK
Forum for Physics Educators