Reddit mentions of The Pleasures of Probability (Undergraduate Texts in Mathematics)

Sounds like a solid book for someone with an undergraduate math background,
https://amzn.com/038794415X
http://www.springer.com/us/book/9780387944159

I've never really found a probability book that I love. Here is the one I had for undergrad:

Pleasures of Probability

It's verbose, but provides excellent coverage of the major stuff. Here's three free ones, but it looks like they jump in a little too quickly:

http://www.math.uiuc.edu/~r-ash/BPT.html

https://web.math.princeton.edu/~nelson/books/rept.pdf

Probability Theory, the logic of science

And an MIT course:

http://ocw.mit.edu/courses/mathematics/18-440-probability-and-random-variables-spring-2011/index.htm

You basically want a strong understanding of:

Conditional Probability, Baye's Thm and it's use, Expectation. And to be familiar with the Law of Large Numbers, Central Limit Thm and Moment Generating functions, and the use of all three.

Freund's Mathematical Statistics is the go-to book for mathematical statistics. It requires a strong grasp of integration techniques (including changing coordinate systems through substitution) and probability.

The graduate level econometrics texts most commonly used are Greene's Econometric Analysis and Hayashi's Econometrics (I have a slight preference for Hayashi)