Subject of Probability Theory
Consider an experiment in which an event $A$ may or may not occur. Examples of such experiments include:
a) Experiment: manufacturing a specific product, Event $A$: the product meets the standard;
b) Experiment: tossing a coin, Event $A$: heads appears;
c) Experiment: shooting five times at a target, Event $A$: scoring 30 points;
d) Experiment: entering a program into a computer, Event $A$: error-free input.
Common to all these experiments is that each can be repeated under certain conditions as many times as desired. Such experiments are called trials. Events are classified into the following types: random, certain, and impossible.
A random event is one that may or may not occur under the given conditions.
A certain event is one that will definitely occur under the given conditions.
An impossible event is one that cannot occur under the given conditions.
For example, if an urn contains only white balls, drawing a white ball from the urn is a certain event, while drawing a ball of another color is an impossible event. Tossing a coin can result in heads as a random event because tails may also appear.
Random events are denoted by capital Latin letters, such as $A$, $B$, $C$, $D$, $X$, $Y$, $A_1$, $A_2, \ldots, A_n$.
Each random event results from many random or unknown causes affecting the event, making it impossible to predict the outcome of a particular trial. However, by repeating the experiment many times under the same conditions, one can identify a certain pattern of occurrence or non-occurrence of the event. This pattern is known as the probabilistic regularity of mass homogeneous random events.
In probability theory, mass homogeneous random events are those that occur repeatedly under the same conditions or when many identical events occur.
For example, tossing one coin 1000 times or tossing 1000 identical coins once is considered the same event in probability theory. The subject of probability theory is the study of probabilistic regularities of mass homogeneous random events.
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