Page 100 - DP-2-2

Design+ Modern interpretations of probability

directions, the condition of equal probability is considered occurrence depends on how frequently that event is
(by default) as an attribute; that is, it is treated as an observed within the context of a broader set of related
inherent attribute of the events within the investigated events. The measure of the possible realization of an event
population. In contrast, in the second one, the probability depends on the frequency of its realization. The more often
is “tied” to the available knowledge (available information) the event is repeated, the higher the measure of its possible
about the events of this population. Consequently, the realization. Such events were later called mass random
first model should be considered idealized and objective, events, because they, firstly, differ from regular events,
while the second is subjective (epistemological). This which appear regularly. Second, they are not unique, single
distinction is essential; thus, not accounting for it can lead events, where the degree of possibility of their realization
to erroneous results. The principle of indifference assumes is senseless and cannot be connected with the frequency
symmetrical consequences of the events under study, that of their realization. On this basis, the interpretation
is, the same probability of their realization. However, in of probability as a relative frequency of realization of a
contrast to the “primary” concept of classical probability, mass random event, namely, the frequency (statistical)
it is not accepted as itself but is established based on interpretation of probability, emerged and began to
analysis (logical, physical, and chemical), which is based develop.
on the available knowledge about the totality of events The frequency (statistical) interpretation of probability
under study. Despite the external difference between the has its roots in ancient science. For many centuries, this
two models of the classical interpretation of probability, idea and the corresponding conclusions associated with it
they both rely on a common basis – symmetry (equal have been used at an intuitive level, applying it in various
probability) of the events of the investigated totality. Only fields of human activity. However, the English scientist
in the first model is symmetry considered an attribute of John Venn first conducted consistent and comprehensive
the events. In contrast, in the second model, it is confirmed studies of this concept and presented them in The Logic
by the available (at the moment) knowledge about the of Chance, published in 1866. Since then, the frequency
investigated set of events. The latter gives grounds to interpretation of probability has been gaining popularity
consider the probability subjective, which is determined among specialists whose activities are related to processing
using the principle of indifference. large arrays of repetitive data (i.e., statisticians). This

Thus, the classical interpretation of the concept of reaction from statisticians is quite understandable because
probability contains internal contradictions. In general, most statistical problems cannot be reduced to a set
this interpretation cannot be taken as a definition of the of events, the probability of realization of which is the
concept of probability, because it points mainly (if not same. Consequently, it is impossible to apply the classical
exclusively) to a method of calculating probability and interpretation of probability.
one that “works” only in particular (simplest or specially According to the frequency interpretation, the
created) situations. At the same time, this interpretation probability is determined through the relative frequency of
played an appropriate constructive role in the history of events directly or indirectly, based on observations of the
mathematics because it started and properly directed corresponding process or the basis of specially designed
the search for answers to the question of the calculation experiments and tests. J. Venn defined probability as a
4
of probability in general conditions, and this led to the limit value of the relative frequency of event realization
formation of a new mathematical theory, which was later at a large number of tests. At the same time, the “large
named probability theory. number” concept was not specified. It was proposed to take
4. Frequency (statistical) interpretation of relative frequency as the primary concept when defining
probability. Since the relative frequency is determined
probability by the practical implementation of the corresponding
The classical interpretation of probability is considered to procedure, this probability is called empirical probability. 7
be related to the analysis of the realization of an act or an The frequency interpretation of probability was further
event, indicating the intentions of the possibility of such developed in the 20 century in the works of Richard
th
realization. However, in practical activity, most of us have Mises (Figure 3 ), who significantly supplemented and
7
to deal with sets (classes) of events, which actualize the expanded Venn’s conclusions. Mises considered probability
task of studying the properties of such sets, leading to a as a mathematical artifact reflecting not finite sequences
different (frequency) interpretation of probability. of observational results, which have corresponding
It is evident (at least there is no substantial reason to properties, that is, first, an artifact was introduced, and
deny it) that the measure of the likelihood of an event’s then a comparison of this artifact with reality was carried

Volume 2 Issue 2 (2025) 5 doi: 10.36922/dp.6387