There are 300 white balls inside a box. We are drawing randomly 100 balls from inside of the box, and we paint those 100 balls with a black color and then we put them back in the box. Afterwards, we are drawing again randomly 100 from inside of the box. What's the probability of getting exact 10 black balls the last time we draw 100 balls?

I really couldn't think of some solution to this, it seems quite different from what i have already solved in probability problems.

  • $\begingroup$ This looks hypergeometric $\endgroup$ – Henry Feb 26 '18 at 14:43
  • $\begingroup$ Have not solved yet problems like: $n$ balls are there of which $w$ are white and $b$ are black. What is the probability of getting exactly $k$ black balls when $m$ balls are drawn? Here $n=300$, $w=200$, $b=100=m$ and $k=10$. $\endgroup$ – drhab Feb 26 '18 at 14:45


  • the ways to select 100 balls are $\binom{300}{100}$
  • the ways to select 10 black balls among the 100 black balls are $\binom{100}{10}$
  • the ways to select the others $100-10$ not black balls among the others 200 balls are $\binom{200}{90}$
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  • $\begingroup$ "...the ways to select the others 100−10 black balls..." Is the word "black" correct in this place? $\endgroup$ – user Feb 27 '18 at 20:46
  • $\begingroup$ @user thanks I fix the typo! $\endgroup$ – user Feb 27 '18 at 20:48

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