Very good article Dave! Probabilities and statistics are indeed highly nonintuitive, i think that's part of the problem when it comes to communicating scientific data to the public.
The Monty Hall problem is another cool example that took me a while to wrap my head around:
https://en.wikipedia.org/wiki/Monty_Hall_problem
RE: The Birthday Paradox and Our Awful Human Intuitions When It Comes to Probabilities and Exponents