# Probability Foundations: Joint, Marginal, Conditional, and Bayes — The Language of How LLMs Think

> Source: https://sukruyusufkaya.com/en/learn/llm-muhendisligi/olasilik-temelleri-joint-marginal-conditional-bayes
> Updated: 2026-05-13T13:00:23.014Z
> Category: LLM Mühendisliği
> Module: Module 1: The AI Engineer's Mathematical Arsenal
**TLDR:** LLMs are fundamentally conditional probability machines. The math of P(x_t | x_<t), joint/marginal/conditional relationship, independence, the power of Bayes theorem, distribution families (Bernoulli, Categorical, Gaussian), expectation, variance — sampling (temperature, top-k, top-p) starts here.