I'm looking for a rigorous introduction to probability to help prepare me for a future course I plan on taking, "Advanced Introduction to Probability". Something possibly like Spivak's, where proofs are key.
Any help is appreciated.
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Introduction to Probability by Dimitri P. Bertsekas and John N. Tsitsiklis
The authors are MIT professors.
Here are probability lecture notes written by the authors themselves.
Here are also video lectures on Youtube by Tsitsiklis. (Thanks @dietervdf for pointing that out.)