In a jar there are two balls: black and white.
We draw one ball every time, chacking his color and return it to the jar with another ball of the same color.
The test is ended after we pick black ball for the first time.
Let $X$ be the number of steps until the end of the test (When a black ball has been picked).
I want to find the distribution
of $X$ and also $E[X]$ which represents the expectation of $X$.
I wanted to use geometric distribution, I just didnt know how to handel with the increasing number of balls.
Thank you