Probability Fundamentals: Events, Distributions and Joint/Conditional/Marginal Probability

~12 min read

The basic vocabulary of probability — events, distributions, and the three ways of asking 'how likely' (joint, conditional, marginal) — that every later ML idea builds on.

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Key points

  • Probability is a number from 0 (never) to 1 (always) that captures how likely an event is
  • A probability distribution lists every possible outcome with its probability, and they all sum to 1 — exactly how an LLM scores its whole vocabulary at each step
  • Joint probability P(A and B) = both things happening; marginal probability P(A) = just one thing, ignoring the other
  • Conditional probability P(B | A) = the chance of B given that A already happened — often different from B's plain probability
  • P(A and B) = P(A) x P(B | A) links all three — the exact formula behind how a language model scores a full sentence