The problem is stated as follows. We have a box with $W$ white balls and $B$ black ones. Repeat $N$ times: each iteration a ball is taken out (uniformly), and put back along with $K$ (constant) more balls of the same color.
Prove that the probability to take out a black ball on the $i$-th iteration is independent of $i$. This is intuitive but I was unable to prove it (tried using induction).
Define the sample space and probability function for the problem of repeating the above iteration $N$ times. The sample space is clear to me (binary vectors of length $N$) but the probability function is hard to define in a closed form.
Moreover, I'm surprised that question 2 did not come before question 1 because to solve 1, we must understand the probability space. Or is it a common approach in probability to define how we want the space to "act" and only then define the space along with the distribution function?