Basic Probability: What Every Math Student Should Know

Probability made approachable

Basic Probability: What Every Math Student Should Know is a tightly focused introduction to elementary probability, written with students in mind. Henk Tijms builds the subject in a way that favors intuition first, then formal detail, which makes the material especially usable for readers who are meeting probability for the first time.

This second edition is aimed at statistics and data science students, but it is also relevant to readers in mathematics, engineering, computer science, and business analytics. The emphasis falls on the ideas that matter most in practice: conditional probability, Bayesian reasoning, the Poisson distribution, simulation, and the foundations that support later work in applied probability.

What the book covers

• Combinatorics and basic calculus as preparation for probability
• Conditional and Bayesian probability
• Random variables, expectation, and standard deviation
• Core distributions, including binomial, hypergeometric, Poisson, normal, uniform, exponential, and bivariate normal
• Central limit theorem, generating functions, and the chi-square test
• Monte Carlo simulation and an introductory treatment of Markov chains

A practical textbook for active study

The structure reflects classroom realities: explained concepts, worked examples, problem-solving strategies, exercises, answers to all problems, and selected worked solutions. That mix makes the book useful not only for coursework, but also for independent study when you want a probability text that teaches by doing rather than by example alone.

Why it stands out

One of the book’s strengths is its balance between theory and application. Real-life Poisson examples, simulation methods, and Bayesian ideas give the mathematics a concrete edge, while the chapter on Markov chains adds a modern touch that broadens the book beyond a standard introductory outline.

If you are looking for a probability ebook that is methodical, accessible, and genuinely geared toward students, this edition offers a smart place to start.