The concept and history of the development of probability

Probability is a branch of mathematics that deals with the analysis of random events. As such, it developed in the 17th century, and its founders were the French mathematicians Fermat and Pascal, who, at the request of a mutual gambling friend, in 1654, provided a solution to a problem related to a card game.

It first appeared in connection with gambling and insurance in the 17th century. A well-defined probability theory was then applied to various problems such as smallpox vaccination, religion, etc. to become an indispensable tool in the social and natural sciences today. In some fields (quantum mechanics), probability is the fundamental concept through which reality is understood.

It can be said that the concept of probability significantly changed the way humans view nature and society. In the 18th and 19th centuries in England and France, the concept of probability became a philosophical response to skepticism. It was understood that humans could not acquire perfect knowledge, but they could learn enough to meet their everyday needs. Laplace argued that humans' reliance on probability was a consequence of imperfect knowledge. A person who knew every particle in the universe with unlimited computing power could know the entire past and predict the entire future.

Probability in the 18th century dealt with causes and effects. Jacob Bernoulli formulated and proved the law of large numbers, which gave a formal structure to reasoning about cause and effect. With this law, he proved that the empirical proportion of some events will tend to the true probability p, as the number of experiments increases. Even if the probability p is not known in advance, someone with sufficient experience can infer it.

During the Enlightenment, there were attempts to incorporate probability into the foundations of a new theory of morality, in the form of judicial and electoral probability (judicial and electoral were formally similar for French mathematicians). The key question was how to be sure that a jury would reach the right verdict. One of the classic topics was the question of the reliability of testimony. Probability has been used to disprove accounts of miracles.

Probability in everyday life

Probability is most often associated with games of chance: lotto, lottery, cards. The characteristics of games of chance are that the outcome of an individual event cannot be predicted with certainty, but the common result resulting from a large number of attempts shows some regularity. For example, if we say that the probability of getting heads in a coin toss is 50%, we still cannot predict the outcome of a single toss, but with high confidence we can predict the overall outcome of a large number of tosses.

Probability is very often mentioned in informal conversation, when we want to indicate the degree to which it is possible for an event to have occurred or to occur, not strictly referring to the mathematical quantification of probability, but more to the concept of uncertainty and imperfect knowledge about the past and future of man.

Probability in statistics

Probability is the connection between two ideas: description of data and inference about the characteristics of a population based on the properties of a sample. Since it studies chance, probability is the foundation of statistical inference, because it is essential to estimate the probability of a random event in order to compare the data collected with the data we expect to obtain from random events.

Statistical inference, as an inductive method, is prone to error. Therefore, such inference would be practically useless in science if there were no way to estimate the degree to which error is possible. Probability is precisely the tool that allows us to determine how reliable a conclusion is made based on the data being tested.