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Probability_ A Very Short Introduction (Very Short Introductions)
A concise tour of probability as the formal study of uncertainty, explaining its core interpretations, mathematical laws, history, and wide-ranging applications to decisions in everyday life, games, science, medicine, law, and finance.
A profile of this book is on the way.
What it’s about
Probability: A Very Short Introduction demystifies the mathematics of chance for the general reader, showing that probability is not a subject that defies common sense but one that sharpens it. John Haigh lays out the three main interpretations of probability—objective (classical), frequentist, and subjective—and the simple but powerful laws (Addition, Multiplication, independence, Bayes' Rule) that let us manipulate them. Through vivid examples ranging from dice, cards, lotteries, and TV game shows to epidemics, DNA evidence, airline overbooking, queues, and stock options, the book shows how probability is 'the very guide to life,' the key to making sound decisions under uncertainty. It also exposes common fallacies—the gambler's fallacy, the prosecutor's fallacy, Simpson's paradox—that trap the unwary, equipping readers to reason clearly when faced with risk.
The through-line
- Who it’s for
- A curious general reader who wants to understand uncertainty and make better decisions in a world governed by chance
- The problem
- Probability is full of trick questions, fallacies, and counter-intuitive results that seem to defy common sense They feel confused or intimidated, fearing that they cannot reason reliably about risk and chance
- The plan
- Learn the three interpretations of probability—objective, frequentist, and subjective
- Master the core laws: Addition, Multiplication, independence, and Bayes' Rule
- Understand distributions, means, variances, and the Law of Large Numbers
- Apply utility and expected value to make rational decisions under uncertainty
- Recognize and avoid common fallacies through careful counting and attention to assumptions
- The payoff
- Confident, clear reasoning about chance and risk · Better decisions in life, money, health, and games · Immunity to common probabilistic fallacies and misleading statistics
See our guide
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Additional reading
- Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences · Cohen, J., & Cohen, P.
The book recommends this text for its excellent, accessible narrative discussions on regression, particularly for explanatory purposes in the social sciences.
- Classical and Modern Regression with Applications · Myers, R.
Cited as an excellent resource for its modern approach to regression analysis, especially its strong treatment of regression diagnostics for checking assumptions and identifying influential data points.
- Multivariate Statistical Methods in Behavioral Research · Bock, R. D.
This text is frequently cited by the author for more advanced or technical explanations of concepts in MANOVA, repeated measures, and step-down analysis.
- The Analysis of Covariance and Alternatives · Huitema, B.
Recommended as a very comprehensive and thorough text for readers wishing to gain a deeper understanding of Analysis of Covariance (ANCOVA).
- Structural Equations with Latent Variables · Bollen, K. A.
The guest-authored chapter on SEM heavily references this book as a key source for understanding fundamental concepts like model identification.
- Hierarchical Linear Models: Applications and Data Analysis Methods · Raudenbush, S., & Bryk, A.
The guest-authored chapter on Hierarchical Linear Modeling (HLM) cites this as the seminal text on the topic and the basis for the HLM software.
- Applied Discriminant Analysis · Huberty, C.
The chapter on Discriminant Analysis introduces this book as an excellent, current, and very thorough resource on the topic.
- Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan · John Kruschke
Recommended for reading 'During this book' to get additional information and a different perspective on Bayesian statistics and modeling.
- Regression and Other Stories · Andrew Gelman, Jennifer Hill, & Aki Vehtari
Recommended for reading 'During this book' as a supplementary text for a broader understanding of regression and Bayesian modeling.
- Statistical Rethinking: A Bayesian Course with Examples in R and Stan · Richard McElreath
Recommended for reading 'After this book' as a next step for readers who have mastered the concepts and wish to deepen their understanding of Bayesian modeling.