The limit of $P(x=r)$ of binomial distribution $x = B(n,p)$ where $n$ tends to infinity is zero. but what if we want to know the limit of $P(x=n/k)$ where $k>1$ and $n/k$ is rounded to the nearest integer?
For example, if $10\%$ of the population likes white chocolate but we take a survey of an unknown but very large sample and want to know what the probability that $15\%$ of the sample likes white chocolate, how would we do it?
My thoughts are that it's related to the poisson distribution but I can't work it out for myself.