Probability of random event is a mathematical concept that quantifies the likelihood of an event or outcome occurring. It is a measure of the uncertainty or chance associated with different outcomes in a given situation.
There are two approaches to determining probability: statistical and axiomatic.

Due to the statistical approach, we have to do a lot of experiments and calculate the frequency of occurrence of the corresponding event:

In accordance with the axiomatic approach, we postulate the value of the probability based on certain properties of the stochastic experiment that we conduct. In the axiomatic approach, we use probability distribution to determine the probability of occurring random events. We will consider exactly the axiomatic approach to determining the probability in this course.

Let's consider some properties of probability:

1. The probability of an event impossible in the context of a particular stochastic experiment equals zero;
2. The probability of the union of all elementary events equals one;
3. As a result of properties 1 and 2, we can say that probability can't be less than 0 and more than 1;
4. If random events do not intersect, then the probability of the union of random events is equal to the sum of the probability of occurrence of each random event separately.

Now let's consider classical probability definition: if all elementary events have equal odds of happening then the probability of occurring of event A can be calculated as follows:

Assume that we have a box filled with balls of two different colors. The balls are mixed so we can assume that the probabilities of drawing a ball of both colors are the same. So we can use the classical probability definition to calculate probabilities of drawing balls of a particular color.