Suppose I have $N$ samples, and 1/4 of them are bad. I draw $n$ samples $(n<N)$, and I want to know what's the probability that less than 1/3 are bad. I know it should use hypergeometric distribution to calculate, that is:
And I understand that if N approaches to infinity, then we can use binomial distribution to calculate the value, that is:
My question is: when $N$ is not infinity, then which probability is greater? Using hypergeometric distribution or binomial distribution? Is there any result in math?