Probability Theory

Explore how probability underpins statistics, guiding data analysis, distributions, and probability distribution functions, and connect random variables to real-world questions. Lay a foundation for future topics and applications.

Master basics of set theory for probability, defining elements and sets, exploring subset and null set notation, and applying complement, intersection, and union operations.

Visualize probability relationships using Venn diagrams with a sample space rectangle and subset circles, illustrating complement, intersection, and union through problem solving.

Learn the basics of probability, including the axioms and the addition rule, and use the sample space, events, and union and intersection with dice examples.

Explore conditional probability, the multiplication rule, independence, and tree diagrams, paving the way to Bayes' theorem and the law of total probability.

Explore a visual recap of conditional probability using a 16-square grid to compute blue and pink outcomes and their conditional relationships, laying groundwork for Bayesian statistics.

Bayesian probability applies Bayes' formula to update the likelihood a text came from Candice given emoji, with 65% Alice, 25% Beth, 10% Candice and emoji rates 5%, 10%, 50%.