A natural introduction to probability theory

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According to Leo Breiman (1968), probability theory has a right and a left hand. The right hand refers to rigorous mathematics, and the left hand refers to ‘pro- bilistic thinking’. The combination of these two aspects makes probability theory one of the most exciting ? elds in mathematics. One can study probability as a purely mathematical enterprise, but even when you do that, all the concepts that arisedo haveameaningontheintuitivelevel. Forinstance, wehaveto de? newhat we mean exactly by independent events as a mathematical concept, but clearly, we all know that when we ? ip a coin twice, the event that the ? rst gives heads is independent of the event that the second gives tails. Why have I written this book? I have been teaching probability for more than ? fteen years now, and decided to do something with this experience. There are already many introductory texts about probability, and there had better be a good reason to write a new one. I will try to explain my reasons now.