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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

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    The question seems not very well posed to me. The "probability greater than" bit should be "probability equal to". Further, the relation with the title is not clear.2011-05-30

1 Answers 1