Probability theory is a voluminous and rather complicated branch of mathematics. During our work we often have to deal with the need to determine the effectiveness and predict the results, say for the construction of marketing strategies and other tasks. This article outlines the essence and basic formulas of probability, which will help to navigate in this mathematical branch and apply it in practice.

WHAT IS PROBABILITY THEORY?
The result of research regarding the effects of randomness and uncertainty on social, behavioral, and physical phenomena is a branch of mathematics devoted to probability theory. Quantitatively, probability is defined by a number from 0 to 1, where 0 means the ultimate impossibility of an event and 1 is one hundred percent certainty that the event will occur. The more this number approaches 1, the greater the probability that certain events will occur. Probability is also measured on a scale of 0 to 100%.

A simple example of probability is a toss-up: a toss-up of heads or tails is equal in probability because there are no other outcomes for such a coin flip. In practice, probability theory is used to model situations where, under the same conditions, we have different results due to the same actions.

The outcome of a coin flip is random. Random events cannot be fully predicted, but they all have long-term patterns that we can describe and quantify with probability.

Let’s consider three basic theories.

Equally probable outcomes.
There is no reason to claim that the probability of one outcome of an event takes precedence over other outcomes. Imagine a vessel with identical balls that have been thoroughly mixed. The player is asked to take out one of the marbles, with the probability of choosing each of the marbles being the same. If a given situation has a number of results equal to n, then the probability of each result is 100%.

Frequency theory
According to this theory, probability is the limit on the relative frequency with which an event occurs under repeated conditions. The statement “the probability that A will happen is p%” in this case means the following: if you repeat the experiment over and over again, independently and under approximately the same conditions, the percentage of time that A will happen approaches p. The relative frequency is calculated solely after the experiments are conducted based on the data actually obtained.

If a number of experiments are performed under unchanged conditions, the relative frequency becomes stable, i.e., it varies within marginal differences. For example, a professional archer has fired 100 shots and hit the target 90 times out of them. His probability of hitting the target under certain conditions is 0.9. If he fired 10511 shots in his career, of which he hit the target 9846 times, the relative frequency is 9846/10511=0.9367. This figure will be taken into account to predict the archer’s result in future competitions.

Subjective theory
This type of probability is used in the decision-making process in order to further predict human behavior. It has no statistical characteristic. In this case, the probability is the level of verification of a certain statement. For example, the appropriateness of investing in various risky projects, participation in the lottery, planning drug stocks in medical institutions, etc. Subjective probability is determined by means of appropriate local expertise.