# Picking balls with replacement

let there be a urn with: $3$ red balls, $4$ white balls, $2$ black balls.
one ball is picked up and returned to the urn, over and over, what is the probability that the first red ball that will be picked, will be before the first white ball.

It is said that we can neglect the black balls, so the answer is $\frac{3}{7}$, why does the black ball can be neglected?

• because it doesn't affect the order that the red and white balls are pulled out – danimal May 18 '15 at 11:36

For example, if you pick a red ball 2 times, and then a black ball 2 times, and then a white ball 2 times $\rightarrow RRBBWW$, that will be the same as you drew red ball 2 times, and white ball 2 times, since the task is only interested in their order$\rightarrow RRBBWW=RRWW$