There is no such thing as "the" application. It is a useful tool in any situation where the future is unknown yet decisions have to be made as to the future. Isn't that almost any area of company management?
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All the time. Statistic is based on the application of probability theory!
Set theory does have many practical business applications. Some of these include how the Turing machine is used in computer science, and the theory of crisis of foundations in math.
No. I am using "normalization" as used in probability theory as application of a normalizing constant to a value, to make it conform to a certain distribution.
Probability theory and distributive theory.
Statistics is used in many places especially when you are the head of a business and you need to calculate probability and things like that.