## TL;DR

Probability theory quantifies uncertainty — fundamental to machine learning, statistics, cryptography, and randomized algorithms. Key concepts: random variables, probability distributions (Bernoulli, binomial, normal, Poisson), expectation, variance, Bayes' theorem, law of large numbers.

## Core Explanation

Bayes' Theorem: P(A|B) = P(B|A) * P(A) / P(B). Used in: Naive Bayes classifiers, Bayesian inference, spam filters. Probability mass function (PMF) for discrete variables; probability density function (PDF) for continuous. Central Limit Theorem: sum of independent random variables approaches normal distribution — reason why normal distribution appears everywhere.

## Further Reading

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