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.
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.
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.