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Design+ Modern interpretations of probability

Conjecturing. The cover of the English-language edition possibility of realization of the events under study. The
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of the book The Art of Conjecturing is shown in Figure 1. 4 concept of the same possibility of realization of events
Significant attention was devoted to the concept of should be attributed to the realm of the ideal, covering the
probability by Pierre-Simon Laplace, who, in his work entire research space (observation), and considered as an
A Philosophical Essay on Probabilities, most fully and idealized model of the corresponding process.
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comprehensively defined the classical interpretation of the Second, there is the existence of a false circle regarding
concept of probability as the ratio of the number of favorable the definition of probability itself. In fact, within the
realizations of some event to the number of all possible framework of classical interpretation, the probability is
realizations of this event, and different realizations of the defined through the same possibility of realization of
event under study should be equally possible (symmetric, events, which essentially means the same probability (equal
equally, or possible). Portrait of Pierre-Simon Laplace is probability) of realization of these events. At the same time,
shown in Figure 2. 6 the introduction of the concept of equal probability, in

Thus, according to the classical interpretation of turn, supposes the existence (preliminary establishment)
probability, its quantitative determination does not involve of the definition of probability.
any empirical study. The analysis of the possibility of To overcome the difficulties of the classical
realization of the corresponding event provides, in advance, interpretation of probabilities, it was proposed to accept
the determination of the probability value that corresponds as true those judgments and conclusions for which there
to such realization (it is due to this feature that the classical are no sufficient grounds for rejection, a notion that was
interpretation of probability is often called a priori). The formulated as the principle of indifference. By this principle,
classical interpretation of the concept of probability, based the probability of the realization of two events is proposed
on the assumption of the equal possibility of separate to be considered the same (regardless of whether this
realizations of the events under study, contains two logical provision is fulfilled in reality), which provided that there
contradictions. are no grounds for the opposite assumption.
First, it is very difficult, or, more precisely, practically A detailed analysis of the principle of indifference
impossible, to guarantee and to check in practice the same (which can be regarded as the principle of the plausibility
of conclusions regarding the properties of the investigated
events) and its usage both in theoretical studies and in
practical activity indicates the existence of two directions
of the classical concept of probability. The first direction
recognizes the identical probability of realization of
all investigated events of a given population under any
conditions, and the second only in the presence of an
additional condition, namely, the condition of fulfillment
of the principle of indifference. In the first of these

Figure 1. Cover of the English-language edition of the book The Art of Figure 2. Portrait of Pierre-Simon Laplace by Johann Ernst Heinsius
Conjecturing 4 (1775). Image obtained from the Wikimedia Commons website. 6

Volume 2 Issue 2 (2025) 4 doi: 10.36922/dp.6387