Chapter 1

Probability and counting

Luck. Coincidence. Randomness. Uncertainty. Risk. Doubt. Fortune. Chance. You’ve probably heard these words countless times, but chances are that they were used in a vague, casual way. Unfortunately, despite its ubiquity in science and everyday life, probability can be deeply counterintuitive. If we rely on intuitions of doubtful validity, we run a serious risk of making inaccurate predictions or overconfident decisions. The goal of this book is to introduce probability as a logical framework for quantifying uncertainty and randomness in a principled way. We’ll also aim to strengthen intuition, both when our initial guesses coincide with logical reasoning and when we’re not so lucky.

1.1 Why study probability? ...

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