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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 ?

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    If your professor is repeating the experiment of drawing a ball (with replacement), your answer is that of a front-row student who sees the numbers marked on each ball and thus can, after a large number of trials, be fairly sure that the urn contains $w$ white balls and $b$ black balls (all numbers have been seen repeatedly). The book's answer is that of a back-row student who sees black and white balls being drawn from the urn but cannot see the numbers but _can_ estimate $P(b)=\frac{b}{w+b}$. So the outcomes are only $2$ for the back-row student but $w+b$ for the front-row student.2012-03-11

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