Overview

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BiteSize Statistics for Absolute Beginners: Probability Rules and Bayes' Theorem is the second course in the BiteSize Stats for Absolute Beginners specialization. It builds the probabilistic reasoning skills that underlie every later course on distributions, sampling, and hypothesis testing: how to compute probabilities from first principles, combine them correctly with the addition and multiplication rules, condition on new information, count outcomes precisely, and update beliefs with Bayes' Theorem. Across five modules, learners progress from the axioms of probability, event types, and Venn diagrams, through the addition and multiplication rules and probability trees, to conditional probability and contingency tables, permutations and combinations, and finally the Law of Total Probability and Bayes' Theorem — including its use in medical testing and fraud detection. Every core lesson pairs a short video walkthrough and reading with a hands-on interactive notebook built around a realistic business scenario, and each module closes with a graded applied lab using a real dataset.

Syllabus

Foundations of Probability

Introduces the vocabulary and axioms of probability — random experiments, sample spaces, and events — and shows how to calculate classical probabilities and interpret them in a business context. Students then classify events as simple or compound, mutually exclusive or not, and exhaustive, before learning Kolmogorov's three axioms and how to read Venn diagrams to compute union, intersection, and complement probabilities.

The Addition and Multiplication Rules

Covers the general addition rule for computing union probabilities and the concept of statistical independence, then the multiplication rule for joint probabilities of dependent and independent events. Students build and read probability trees to solve multi-stage sequential problems, culminating in a lab that models a two-stage quality inspection pipeline.

Conditional Probability and Contingency Tables

Covers the complement rule for efficiently solving 'at least one' problems, then introduces conditional probability as a restriction of the sample space and the formula that connects it to joint and marginal probabilities. Students build contingency tables and extract marginal, joint, and conditional probabilities, closing with a lab that investigates a counterintuitive fraud-detection scenario.

Counting Methods: Permutations and Combinations

Covers the Fundamental Counting Principle for multi-stage sequential choices, then permutations for ordered arrangements and combinations for unordered selections. Students learn to select the correct counting formula for a given business problem and combine multiple formulas in multi-stage counting problems, closing with a lab spanning scheduling, security, and portfolio-construction challenges.

Bayes' Theorem and Applications

Introduces the Law of Total Probability for computing unconditional probabilities from conditional rates, then derives Bayes' Theorem for updating beliefs given new evidence. Students apply Bayes' Theorem to medical testing (sensitivity, specificity, PPV, NPV) and business contexts (fraud detection, churn, spam filtering), including sequential updating, closing with a lab on sequential quality testing across suppliers.