# Find the probability of drawing at least one white ball

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?

• Try to find the probability of the complement : of drawing no white balls at all. – 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 $$n+m \choose k$$