How Do You Estimate the Number of Elements with a Specific Property in a Sample?

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Suppose I have a total population with x/y percent having a certain property q. If I take an n-number sample of this population, what is the most likely number of elements in this sample that will have property q?

I want to say the fraction z/n will be as close to x/y as possible where z is the number of q-elements in our sample. Any thoughts on how to prove this?
 
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You want to maximize the binomial distribution.
 
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