Say you have $n$ red balls and 1 green ball in a bag. If you take out a red ball you leave it out and if you take out a green ball you replace it. What is the expected number of green balls you would have taken out after $n$ trials?
As I understand this question would be simple to solve if the green ball wasn't replaced either, but since it is I'm not sure how to approach the problem.
Hint:
(Since there is only one green ball, this probability is unaffected by whether the green ball is replaced or not)