Wildlife preservers caught some tigers, tagged and released them. They later caught a second sample of exactly the same size and found that 10% of tigers had tags. According to their calculations , approx 2000 tigers were in the forest. How large was the sample of tigers that they collected.

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These problems are solved with proportions.  Normally, you would solve for how many total animals are there.  But, that's ok.  The formula:

how many total tags/how many total animals =

            how many tags you "recatch"/how many animals you recatch

These ratios have to be equal.  We know know "how...

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These problems are solved with proportions.  Normally, you would solve for how many total animals are there.  But, that's ok.  The formula:

how many total tags/how many total animals =

            how many tags you "recatch"/how many animals you recatch


These ratios have to be equal.  We know know "how many total animals", 2000.  We also know that the right ratio would be 1/10 (for 10%, 10% of the "recatch" had tags).  So:

x/2000 = 1/10

10x = 2000

x = 200

So, there were 200 animals who were tagged.

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We assume that the samples taken are completely random.

Then the original sample was one tenth of the population. (They tagged some percentage of the total population -- the next random sample of the same size found 10% had been sampled before, so the tagged specimens are 10 percent of the population.)

Thus the sample sizes are 2000/10=200.

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