Module 2 · Probability Foundations · Topic 1
Probability. Probability is a number between 0 and 1 that measures how likely an event is to occur. A probability of 0 means impossible, and 1 means certain.
Three Approaches. Classical probability assumes equally likely outcomes (e.g., dice). Empirical (relative frequency) probability uses observed data. Subjective probability is based on personal judgment or expertise.
P(A) = number of favorable outcomes / total number of equally likely outcomes
P(A | B) = P(A and B) / P(B) — Probability of A after restricting attention to cases where B occurred.P(A | B) = P(B | A)P(A) / P(B) — Updates a prior probability after observing evidence.Drawing a heart from a standard deck: P(heart) = 13 hearts / 52 cards = 1/4 = 0.25.
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