Probability book or video for purely analytical brain

Question

That's it. I suck at probability theory. I simply don't seem to get it. The thing is, I have strongly analytical brain, but every single book that I ran to, taught probability using synthesis and not analysis.

Since probability theory is crucial for every programmer and I want to improve, could you tell me the book or video lecture that teaches probability for those unfortunate who has purely analytical brain? I mean I need some fact being presented and then reasons for using this and not that formula or some example presented with explanation what's going on one bite at a time as oppose to building up from small pieces.

I have seen previous questions about probability books here and here but this does not actually answer my question.

Answer 1

If you want a very analytical presentation of probability, you could get a book on measure-theoretic probability. This approach sweeps nothing under the rug. Everything is proven in detail with no hand waving. However, these books require a lot of mathematical background to read. If you'd like to give it a shot, here are a couple popular measure-theoretic probability books.

Probability and Measure

A Probability Path

Answer 2

For me UCLA Probability for Life Science video lectures were very helpful. They really guide you from the first basic steps and help you get real understanding.. I generally think YouTube is a good place to look for lectures these days (-: