Probability forms the mathematical foundation of statistical inference, enabling us to quantify uncertainty and make rigorous predictions from data. It operates within a formal framework where events in a sample space are assigned numerical measures between 0 and 1, governed by Kolmogorov's axioms. Understanding probability is essential not only for modeling randomness but also for grasping how distributions, expectations, and limit theorems converge to make statistical methods work—key insight: probability bridges the gap between theoretical models and real-world variability.

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