Which of the following theories directly pertains to the study of random events?

Probability Theory is the branch of mathematics that specifically deals with the analysis of random events and uncertainty. It provides the framework for understanding how likely an event is to occur under varying conditions. Probability Theory allows mathematicians and scientists to quantify and predict outcomes of random phenomena, enabling the evaluation of events in both theoretical and practical applications.

For instance, it involves concepts such as random variables, probability distributions, and statistical inference, all of which are essential for analyzing situations where outcomes are not predetermined. This theory forms the basis for fields like statistics, finance, and many areas of science, giving tools to make informed decisions in uncertain situations.

In contrast, Linear Algebra focuses on vector spaces and linear mappings, Real Analysis involves the study of real numbers and functions, and Vector Theory pertains to properties and operations involving vectors. While these mathematical disciplines are valuable, they do not specifically address the principles governing randomness and uncertainty in the way that Probability Theory does.