In the applications of probability theory to physical problems, the identification of experimental outcomes is not always unique. We shall illustrate this ambiguity with the die experiment as might be interpreted by players X, Y and Z. X says that the outcomes of this experiment are the six faces of the die forming the space F {f1,…f6}. This space has 26 = 64 subsets and the event {even} consists of the three outcomes f2, f4 and f6. Y wants to bet on even or odd only. He argues, therefore, that the experiment has only the two outcomes even and odd forming the space F = (even, odd). This space has only 22 = 4 subsets and the event (even) consists of a single outcome. Z bets that one face will show and the die will rest on the left side of the table. He maintains, therefore, that the experiment has infinitely many outcomes specified by the coordinates of its centre and by the six faces.

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