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 various interpretations and definitions of probability, including classical, frequentist, and subjective approaches.

One of the fundamental concepts in probability theory is the idea of a random variable, which is a variable whose possible values are outcomes of a random phenomenon. Random variables can be discrete, taking on a countable number of values, or continuous, taking on an infinite number of values within a given range. Probability distributions describe how probabilities are assigned to these outcomes, allowing for the calculation of expected values, variances, and other statistical measures.

Understanding probability is crucial for making informed decisions in uncertain situations, as it helps to model and predict the behavior of complex systems in various domains, from finance to healthcare and beyond ²³⁴.