As an exercise in elementary probability theory, we had to determine the probabilistic models of extracting a ball from a box with $b$ black and $w$ white balls (this was exactly how the exercise was formulated).
Now I solved the exercise, by saying that $\Omega =\{x_1,\ldots,x_b,y_1,\ldots,y_w \}$ and with $p(t)=\frac{1}{b+w},\ t\in \Omega$
But in the solution to the exercise, it was indicated that $\Omega=\{b,w \}$ with $p(b)=\frac{b}{b+w},p(w)=\frac{w}{b+w}$.
Now my question is: Who was right ? Or - are we both right ?
My guess is that I modeled the case where we can distinguish the balls whereas in the solution the case is modeled, where one can't distinguish the balls (this case being a special case of mine, since p(\text{"white"})=w\cdot \frac{1}{b+w}=\frac{w}{b+w}. Am I correct ?