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SCIENCE AND EDUCATION IN THE MODERN WORLD



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SCIENCE AND EDUCATION IN THE MODERN WORLD: 
CHALLENGES OF THE XXI CENTURY"
 
ASTANA, KAZAKHSTAN, FEBRUARY 2023 
44 
examples that experiences lead to events, and that experiments and tests are required to produce 
events. The definition of "probability" served as the base for categorizing events. If we give the 
likelihood of a specific event a numerical value which means giving a 1 to each specific event 
and a 0 to the non-event, then each specific event corresponds to one specific numerical value 
from the range (0;1).The definition of probability is formulated as: 
𝑃(𝐴) =
𝑚
𝑛
,where n is the total 
number of all equally possible, elementary outcomes of this trial, and m is the number of 
elementary outcomes that favor the event. 
For example,the outcome of tossing a coin can be either heads or tails,(n=2,m=1) since 
both outcomes are simple and equally likely, they can be grouped together to represent the total 
number of outcomes. The result (heads) favors the event. As per the standard definition of 
probabilities:
𝑃 =
𝑚
𝑛
=
1
2
Similar to this, when a die is rolled, a complete group of elementary equally possible 
outcomes may appear (n=6,m=1), and the event is favored by a single outcome (rolling a five). 
As a result: :
𝑃 =
𝑚
𝑛
=
1
6

It's customary to use fractions of one, and it's obvious that the probability can change 
within a 
0 ≤ 𝑃 ≤ 1
. In addition, if 
𝑃 = 0 
,it is impossible, if 
0 < 𝑃 < 1 
it is a random event
and if 
𝑃 = 1
, then it is reliable. 
Teaching former students to "apply to stories" is beneficial, depending on the story's 
theme. They are interested in the connections between events and related, contentious issues in 
this area. "Event A leads to the event B," and "Event B is a component of event A" are 
expressions that describe the relationship between the events (
𝐴 ⊂ 𝐵
). The concept of equal 
events can be established logically based on this relationship. Euler-Venn diagrams should be 
used to represent the connections between events and actions. 
Using what they have learned from the theoretical articles, the students compare the 
methods used in the events. Only definitions of actions used to describe events and locations can 
be used to determine it. creation of a utility theory and personal data term correspondence table. 
In order for students to develop their skills in the theory of experiments course, applying 
actions to events and managing the properties of actions are of utmost importance. Based on 
their knowledge of set theory, the students will contrast how operations on sets and events.The 
only distinction between the definitions of operations applied to events and sets is one of 
terminology. Consequently, it is helpful to create a table of correspondence between the terms 
used in set theory and probability theory. Students' ability to solve problems from probability 
theory courses is greatly influenced by how they apply operations to events and how well they 
understand the properties of operations. 


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