Probability theory is a branch of mathematics that deals with the analysis of random events and uncertainty. It provides a framework for quantifying the likelihood of various outcomes, which is essential in fields such as statistics, artificial intelligence, and data science. The theory encompasses different interpretations of probability, including classical, frequentist, and subjective approaches.

In classical probability, the likelihood of an event is determined by the ratio of favorable outcomes to the total number of possible outcomes, assuming all outcomes are equally likely. For example, when rolling a fair die, the probability of rolling a prime number can be calculated based on the number of prime outcomes (2, 3, 5) over the total outcomes (1 to 6) ¹.

Frequentist probability, on the other hand, is based on the long-run frequency of events occurring after many trials. For instance, if you toss a coin 1000 times and observe 600 heads, the probability of getting heads is estimated as 0.6 ².

Understanding these concepts is crucial for applying probability in real-world scenarios, where uncertainty is prevalent ⁴.