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:
Why can we make "so and so" assumptions when we use "some" probability model?
What assumptions does the Poisson make about events, and why do they make sense?
What really is the probability of an event occurring? Does the definition change depend on the situation
Are probabilities total number of successes divided by total number of trials?
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?
What are probabilities?
Additionally, questions like:
- 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.