Which theory deals with the analysis of random phenomena?

Probability Theory is the area of mathematics that focuses on analyzing random phenomena. It provides a framework for quantifying uncertainty and for making predictions about the likelihood of various outcomes. This theory is foundational in various fields such as statistics, finance, science, and engineering, where understanding the randomness inherent in processes is crucial.

In Probability Theory, concepts such as events, sample spaces, probability distributions, and expected values are key tools used to model real-world scenarios influenced by chance. For instance, it allows for the calculation of the probability of specific outcomes occurring based on known information or assumptions about the random processes.

The other areas mentioned have distinct focuses: Linear Algebra deals primarily with vector spaces and linear mappings between those spaces, Function Theory involves the study of complex functions, particularly in the context of complex analysis, and Trigonometry focuses on relationships involving angles and lengths in triangles. None of these disciplines directly tackle the analysis of randomness and uncertainty in the same way that Probability Theory does.