A box contains m white and n black balls. Suppose k balls are drawn from the box. Find the probability of drawing at least one white ball.

Could you help me to solve this problem?

  • 1
    $\begingroup$ Try to find the probability of the complement : of drawing no white balls at all. $\endgroup$ – drhab Oct 7 '18 at 20:23

\begin{align} P(\text{atleast 1 white}) &= 1 - P(\text{no white})\\ &=1 - \frac{n \choose k}{n+m \choose k} \end{align}

If no white balls are chosen, then we can choose $k$ balls from $n$ black balls in $n \choose k$ ways. Total number of ways of choosing $k$ balls from $n$ black and $m$ white is $n+m \choose k$

  • $\begingroup$ Can you explain further. So this involves permutation? $\endgroup$ – James Warthington Oct 7 '18 at 20:25
  • $\begingroup$ @JamesWarthington Added some explanation. Hope it helps $\endgroup$ – sc_ Oct 7 '18 at 20:30

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