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Thanks for reading - this is a book recommendations question. I'm looking for books that deal with probability conceptually.

For example, I'd like books that address questions like:

  1. Why can we make "so and so" assumptions when we use "some" probability model?

  2. What assumptions does the Poisson make about events, and why do they make sense?

  3. What really is the probability of an event occurring? Does the definition change depend on the situation

  4. Are probabilities total number of successes divided by total number of trials?

  5. Are they the number of "equally likely" things that can happen (whatever "equally likely" means) divided by the total number of things that can happen in some situation?

  6. What are probabilities?

Additionally, questions like:

  1. When should we apply "so and so" probability model, and why does it make sense to apply it here?

Note that the "why" is bolded - that's the most important part.

It can be mathematically rigorous (although if it's more philosophical that's fine too), but at the same time, I'm looking for a book that analyzes the conceptual underpinnings of probability theory intuitively.

Thanks!

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  • $\begingroup$ Part 1 of All of Statistics by Wasserman is good. If you want a bit more measure theory, Knowing the Odds By Walsh is good. If you want a very theoretical perspective (probably not much intuition), Probability and Measure by Billingsley is good. $\endgroup$ – parsiad Aug 21 '19 at 23:32
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Good Thinking, by I.J. Good is a great book for you. The author analyzes the conceptual underpinnings of probability theory and brings a philosophical perspective to the theory. There is also a focus on applications.

A little about the author, who worked with Alan Turing at Bletchley Park:

https://en.wikipedia.org/wiki/I._J._Good

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  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$ – The Count Aug 21 '19 at 23:55
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    $\begingroup$ The OP asked for an insightful book and I gave them one. How does it not provide an answer? $\endgroup$ – geocalc33 Aug 21 '19 at 23:59
  • $\begingroup$ It is only my opinion, but you could explain why the book is good for him, for example. $\endgroup$ – The Count Aug 22 '19 at 0:02

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