A First Course in Probability

A sufficient book to pair with a university course. I found it too often fell back on "present a fact/theorem/&c. and prove it" without explanation, justification or illumination. Maybe too focused on being rigorous and correct for the math major, and just hoping the science major will absorb the information with hundreds of different dry examples.

Undergraduate text with lots and lots of really good examples.

This is a great text, Each chapter contains dozens of problems. There's even a special section for "theoretical problems". THere are some hints at the back of the book which I definitely needed. Probability is really an unintuitive subject so doing loads of tough problems is a good way to learn.