[chuankl]

I am not the person you asked, but I have been on a similar path to improve my statistical literacy. For context, I am fairly good at math generally (used to be a math major in college decades ago; didn't do particularly well though I did graduate) but always managed to get myself extremely confused when it comes to statistics.

In terms of books: there are a few good ones aimed for the general public, such as The Signal and The Noise. How to Measure Anything: Finding the Value of Intangibles in Business is a good book of applying statistical thinking in a practical setting, though it wouldn't help you wrap your brain around things like the Monty Hall problem.

The one book that really made things click for me was this:

Probability Theory: The Logic of Science by E. T. Jaynes

This book is a bit more math-heavy, but I think anyone with a working background in a science or engineering field (including software engineering) should be able to get the important fundamental idea out of the book.

You don't need to completely comprehend all the details in math (I surely didn't); it is enough to have a high-level understanding of how the formulas are structured at the high level. But you do need enough math (for example, an intuitive understanding of logarithm) for the book to be useful.