Introduction to Probability

This part introduces the probability concepts that support the rest of the handbook. The goal is practical understanding: how uncertainty is defined, how conditional reasoning works, and how these ideas translate into classification and inference workflows.

You can complete this part with the interactive apps only. R and RStudio are optional for users who want script-based replication.

How This Part Is Structured

Block	Purpose	Main chapters
Foundations	Define probability, events, and conditional probability	Definitions of Probability, Jeffreys’ axiom system
Bayesian reasoning	Apply conditional probability to posterior updating and diagnostic interpretation	Bayes’ Theorem, Sensitivity and Specificity
Applied classification	Use probability for text classification and smoothing logic	Naive Bayes Classifier
Asymptotic intuition	Understand convergence of sample averages	Law of Large Numbers
Integrated practice	Consolidate concepts through exercises	Problems

How To Use It

If you are new to probability, read the chapters in order.
If your focus is applied diagnostics or classification, start at Bayes’ Theorem and then return to the foundations as needed.

After this part, move to Probability Distributions for distribution-specific models, and use Appendix A — Method Selection Guide (Appendix A) when you need a fast method choice.