Probability theory studies the objective patterns of mass random events. An event is something that may or may not happen when a certain set of conditions are met. Among the possible events, there are reliable and impossible ones. If some event happens for sure, it is called true. If some event clearly cannot happen when it is called impossible (Lalo & Rohatgi, 2020). If an event is unreliable or impossible, then it is often called random. In everyday life, at work, people can meet with probability theory and understand the mechanism of its work in practice.
The most striking example of applying probability theory in life is almost any kind of game. Playing cards with a friend, I calculated the probability of my victory through probability theory. I needed to understand the likelihood that, for example, an even number would fall out ten times in a row. In this case, it is necessary to multiply 0.5 to 0.5 and do it ten times. Next, it is needed to multiply by 100%, and the result will be only 0.097% or about one chance out of 1,000. In other words, the chance of the desired number falling out is almost zero.
Another example from life is the situation with exam preparation. Once, we were asked to learn 50 tickets, but I started preparing late and learned only 45 out of 50 tickets. Then I calculated the probability of losing one of the 45 tickets that I learned on the exam. Thus, 45:50 turns out the answer is 0.9, that is, almost one, which means the probability is high enough that I will be able to pass the exam considering how many tickets I learned successfully.
Reference
Laha, R.G., & Rohatgi, V.K. (2020). Probability theory. John Wiley & Sons.