We start with an urn that has $i$ white balls. At each step we draw $1$ ball. If it is white, we return a black ball. If it is black, we return this black ball.
1) What is the probability of drawing a white ball at the $n$-th step? - Checking the decision tree I found that $(1-1/i)^{n+1}$ works. But why?
2) How many white balls have been drawn at the $n$-th step? - Go via cumulative distribution function?
Thanks :)