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OK, so I'm learning probablilites for the first time, and of course I'm having lot of conceptual difficulty (eg How does the outcome depends on how you define randomness, why for example Monty Hall problem is true).

Can you suggest some good probability book which doesn't hand waves these issues, and treats probability from a historical viewpoint, and also readable by beginners ?

(BTW, I have the book ""40 Puzzles and Problems in Probability and Mathematical Statistics"" for intersting and hard exercises, but you can suggest some hard and challenging problem book also as a sidenote)

(Sorta analgous to Hardy's book A course in pure mathematics for learing calculus)

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  • $\begingroup$ A major issue with probabilities is defining an appropriate framework in which probabilities make sense. We have an intuitive sense of probabilities, but our intuition can quickly lead us astray. The appropriate framework usually includes measure theory, integral, etc, which typically takes some degree of sophistication. Hence readable by beginners and no hand waving might be a tough request. $\endgroup$ – copper.hat Oct 21 '17 at 19:19
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I highly recommend Fifty Challenging Problems in Probability with Solutions by F. Mosteller, available quite cheaply in Dover.

In general, probability is very appealing but can be quite tricky. I do not know of a historical treatment, but I would recommend a more advanced text by J. Pitman, called Probability. You might also try Bertsekas and Tsitsiklis's text from MIT, called Introduction to Probability; you can find older versions on the web.

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