Module 2 · Probability Foundations · Topic 2
Sample Space. The sample space (S) is the set of all possible outcomes of an experiment. An event is a subset of the sample space.
Simple vs Compound Events. A simple event has exactly one outcome (e.g., rolling a 4). A compound event consists of two or more simple events (e.g., rolling an even number = {2, 4, 6}).
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.Flipping two coins: S = {HH, HT, TH, TT}. The event “at least one head” = {HH, HT, TH}. P(at least one head) = 3/4.
For complex experiments, use a tree diagram or systematic list to enumerate all outcomes. This ensures you don’t miss any possibilities.
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