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I've encountered the following interview question:

A field with unknown number of rabbits. Catch 100 rabbits and put a label
on each of them. A few days later, catch 300 rabbits and found 60 with 
labels. Estimate how many rabbits are there? 

Can anyone tell me how to do this?

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  • $\begingroup$ capture-recapture problem which can be easy and difficult. $\endgroup$ – Deep North Sep 7 '15 at 4:45
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I can give you a hint:

Recall that if you have a finite population with $n_1$ subjects from group 1 and $n_2$ subjects from group 2, if you were to randomly sample a subject from the population, the probability that you get a subject from group 1 is

P(random sample from group 1) = $\frac{n_1}{n_1 + n_2}$

In this case, which of these values are known and which do you have estimates for?

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  • $\begingroup$ Good one with some assumptions. $\endgroup$ – Deep North Sep 7 '15 at 4:47
  • $\begingroup$ @CliffAB, thanks so much. Assume that there are x rabbits in total. So P(sample a labeled rabbit) = 100/x. E(sampling 300 times) = (100/x)*300 = 60 ==> x = 500. Am I right? $\endgroup$ – FihopZz Sep 7 '15 at 11:12
  • $\begingroup$ Looks right to me! $\endgroup$ – Cliff AB Sep 7 '15 at 15:13

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