Conditional probability of picking balls Suppose that a bag contains $11$ black balls and $9$ white balls. A child takes out a ball $6$ consecutive times, each time replacing the one taken (with a ball of the same color). Find the probability of that he takes out $5$ black balls given that exactly $2$ of the first $3$ times he takes out balls, they were black?
I have absolutely no idea how to approach this problem. It mentions that replacement is involved which implies that binomial distribution may be used. Any assistance is much appreciated.

Hints:

*

*The verbiage about replacement simply means that just before each draw of a golf ball, there are exactly 11 black and 9 white balls.


*The given condition that 2 of the 1st 3 draws are black reduces the problem to asking what are the chances that the next three draws are all black.  In other words, the original problem + the assumed event equate to the alternative problem of : what are the chances that the first 3 draws are all black.
