tõenäosusi

**Tõenäosusi** (probability) is a branch of mathematics that deals with the analysis of random events and their likelihoods. It quantifies how probable certain outcomes are within a given set of conditions, providing a framework for understanding uncertainty in both theoretical and practical contexts.

Probability theory has its foundations in the 17th century, emerging from early studies of games of chance and insurance. Key concepts include sample spaces—the set of all possible outcomes—and events, which are subsets of these outcomes. The probability of an event is measured as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Basic probability rules, such as the addition and multiplication rules, govern how probabilities of combined events are calculated.

Applications of probability are widespread, spanning fields like statistics, finance, machine learning, and natural sciences. In statistics, probability helps infer data patterns and make predictions, while in finance, it underpins risk assessment and investment strategies. Random processes, such as those in physics or biology, are often modeled using probability distributions, which describe the likelihood of different values occurring.

Mathematical probability is distinct from empirical probability, which estimates likelihood based on observed frequencies. Theoretical probability, on the other hand, relies on logical reasoning and assumes equal likelihood for all possible outcomes in a fair scenario. Modern probability theory also incorporates advanced topics like measure theory and stochastic processes, which extend its reach into complex systems.

Understanding probability is essential for decision-making under uncertainty, enabling individuals and institutions to evaluate risks and opportunities systematically. While probability does not predict exact outcomes, it provides a quantitative tool for assessing the chances of different results, making it indispensable in both academic and real-world applications.