# Urn probability problem

Hey guys I was struggling with this question and was looking for some help:

An urn contains 10 red and 10 white balls. The balls are drawn from the urn at random, one at a time. Find the probabilities that the fourth white ball is the fourth, fifth, sixth, or seventh ball drawn if the sampling is done with replacement?

I know that the probability that it's the fourth ball drawn to be $(\frac{1}{2})^4$

But the book says that on the fifth ball drawn the probability would be $(\frac{1}{8})$ and I'm not exactly sure why. Any help would be appreciated!

Thanks!

• Hint: to get it on the fifth trial you need to have drawn one R and three W (in some order) in the first four. First compute the probability, $p$, of that. It follows that the probability of getting the fourth W on trial five is $\frac p2$. – lulu Sep 28 '15 at 19:47

Hint: $RWWWW, WRWWW, WWRWW, WWWRW$