WHICH BOX? WHICH BALL?

Figure: A sketch of the six boxes of the toy experiment. The index refers to the number of white balls.

The `game' begins by showing six boxes (Fig. 1), each containing five balls.One box has only black balls, another four Black and one White, and so on. One box, hereafter `B$_?$', is taken at random out of the six and we start the game. At each stage, we have to guess which box has been chosen and what color ball will be selected in a random extraction. We then extract a ball, observe its color and replace it into the box (1).

From the point of view of measurements, the uncertain number of white balls plays the role of the value of a physical quantity; the two colors the possible empirical observations. The fact that we deal with a discrete and small set of possibilities, both for the `measurand' and the empirical `data', only helps in clarifying the reasoning. Moreover, one of the rules of the game is that we are forbidden to look inside the box, in the same way that we cannot open an electron and read its mass and charge in a hypothetical label inside it.