Chance, Luck, and Statistics: The Science of Change by Horace C. Levinson PDF

By Horace C. Levinson

ISBN-10: 0486210073

ISBN-13: 9780486210070

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Extra info for Chance, Luck, and Statistics: The Science of Change

Example text

But we also obtain a total of 7 if we turn up the ace on the red die and the six spot on the blue die. Thus there are two favorable combinations involving the ace and the six spot. This simple fact, so obvious when the dice are thought of as painted different colors, was once a real stumbling block to the theory of probability. If we continue the listing of the 48 THE GRAMMAR OF C H A N C E favorable cases, we can write the complete list in the form of a short table: TABLE I Blue 1 6 2 5 3 4 Red 6 1 5 2 4 3 Each line of this table indicates one favorable combination, so that there are six favorable cases.

This doctrine is based on the following reasoning: (a) I n the long run the numbers come u p equally often; (b) the 5 has appeared less often than the other numbers; therefore (c) the 5 should appear more frequently than the other numbers, until the "equilibrium" is restored. Unless we succeed in making clear the fallacy in this reasoning, there is little use in discussing the theory of games of chance, or statistics and their applications to science and business. I n particular, we shall need a clear understanding of the matter when we come to the question of "systems" in roulette.

However, in all of the problems we shall consider later on, the possible cases will impress us as so obviously similar that our skepticism is not likely to be aroused unduly. There is a difficulty of a logical order in this definition of probability, due to the occurrence of the words equally likely as applied to the possible cases. Equally likely cases would seem to be those whose probabilities are equal, thus making the definition of probability depend on the idea of probability itself, a clear-cut example of a vicious circle.

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Chance, Luck, and Statistics: The Science of Change by Horace C. Levinson


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