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I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one with good problems and clear rigorous style?

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Let me start the ball rolling: here is a text book that I use and it has wonderful examples, and it really pushes me (not saying much) but it is undergrad level at least Grimmett prob. And random processes

Chinny84
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