This is the question:
In a box, George has $m$ batteries of which $n$ are dead. He tests them randomly and one by one. Every time that a good battery is drawn, he will return it to the box; every time the dead battery is drawn, he will replace it by a good one.
(i) Determine the expected value of number of good batteries in the box after $n$ of them are checked.
(ii) Determine the probability that on the $n$th draw George draws a good battery.
Will anyone please give me an idea on how to begin solving this problem?
The question sequence seems to be awkward to me. Would I calculate the probability of getting a good battery on nth draw before trying to figure out the expected value?
Even so, I seem to have trouble formulating probability of drawing a good battery on the $n$th draw.