why is probability not considered part of pure mathematics? wikipedia considers probability a part of applied mathematics, and it doesn't seem to fall under one of the four areas of mathematics (algebra, number theory, topology/geometry,analysis).
Nevertheless it seems to me to be a very fundamental mathematical concept, so why is it not considered a part of pure mathematics?

The way I interpret the applied and pure dichotomy in math is:
Applied math is taking established mathematical results and utilizing them in describing, understanding and solving real-world problems.
Pure math is a collection of mathematical results that serve the purpose describing, understanding and solving abstract problems. That is, problems which aren't a real-world problems.
They are not absolutely disjoint but rather are important parts of the whole of mathematics. Moreover, despite my above "definitions", I would say there is no strongly distinct line between the two. A research paper could have both pure math results and applied math results within it.
Probability falls under measure theory which is part of analysis, but also has the ability to be applied to real-world problems. I would say it is both.
