An urn contains black balls and white balls.
We know that if we draw randomly with replacement, for example $N = 100$ balls, we have a probability greater than $P$ (example $P= 0.60$) to get more than $k$ (example $k = 33$) black balls.
What is the minimum initial percentage $R$ of the number of black balls contained in the urn by the total number of balls?
Is there an explicit formula $R(N, k, p)$ giving $R$ as a function of $N,\;k,$ and $p$?
Same questions if we perform the draw of the $N$ balls without replacement