Mutually exclusive events are those that cannot occur at the same time—like flipping a coin and getting both heads and tails simultaneously. Every machine learning algorithm relies on these principles to update beliefs based on new data.
Probability Axioms Bayesian Inference Basics
In the context of probability theory, these axioms were rigorously formalized by the Russian mathematician Andrey Kolmogorov in the 1930s. Those are theorems, not axioms; they are conclusions derived from the axioms above.
Ensuring that models adhere to these axioms guarantees that the outputs remain logically sound and mathematically valid. For such events, the probability of either event occurring is simply the sum of their individual probabilities.
Probability Axioms Bayesian Inference Basics
His formulation provided the rigorous mathematical framework that transformed probability from a collection of intuitive tricks into a coherent branch of mathematics. The Mechanics of Combination While the first axiom sets the stage, the second and third axioms govern how probabilities behave when we combine events.
More About What are axioms of probability
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More perspective on What are axioms of probability can make the topic easier to follow by connecting earlier points with a few simple takeaways.
