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Probability axioms, also known as Kolmogorov's axioms, are a set of rules that form the foundation of probability theory. They were first proposed by Russian mathematician Andrei Kolmogorov in the 1930s. These axioms provide a mathematical framework for describing and analyzing random events and phenomena.

The three probability axioms are as follows:

1. The probability of an event is a number between 0 and 1, inclusive. This means that the probability of any event must be non-negative and no greater than 1.

2. The probability that an event will occur is equal to 1 minus the probability that it will not occur. This is known as the law of complementary probabilities.

3. The probability that a set of mutually exclusive events will occur is equal to the sum of the probabilities of each individual event. This is known as the addition rule for mutually exclusive events.

These axioms are widely used in many fields, including statistics, engineering, economics, and finance. They provide a rigorous and consistent framework for making probability statements and predictions about real-world events.

The importance of these axioms lies in their ability to limit the possible values of probability distributions and to ensure that they are consistent and coherent. They have been widely used in the development of various probability models and theories, such as the laws of large numbers, the central limit theorem, and the concept of random variables.

The probability axioms have been extensively used in practice to model and analyze complex systems, to make predictions about future events, and to make informed decisions under uncertainty. They remain a fundamental building block of probability theory and are still widely used today in many different areas of application.