Suppose there is an Urn with $n$ balls, $m$ being white and $(n-m)$ being black.

Now we draw $c, c < n$ balls - any white ball drawn will be colored black - then we put all balls back into the Urn and repeat.

How often do we need to draw until we expect all balls to be black?

//- More clearly: how often do I need to draw until 95% of the white balls are colored in black?

  • 1
    $\begingroup$ Forget about the colors, there are $m$ special balls, and we repeat our draws until we have drawn each of them at least once. $\endgroup$
    – vadim123
    Nov 17 '14 at 18:59
  • $\begingroup$ What is the exact meaning of "we expect all balls to be black"? Probability over $\frac12$? Probability one? $\endgroup$ Nov 17 '14 at 19:03
  • $\begingroup$ @JoonasIlmavirta : I need a finite solution: e.g. when are 95% of the former white balls black. Sorry for being unclear $\endgroup$
    – juq
    Nov 17 '14 at 19:18

The expected number of draws to choose a white ball given there are $m$ of them is $\frac{n}{m}$, and now we must choose one of the $m-1$ remaining white balls, etc. until there are none left so the expected number of draws is:



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.