Yes, probabilities always can make the human brain hurt LOL. In fact Ive seen people get so angry as to almost throwdown over the Monty Hall Problem. They just cannot get it because it doesn't seem right.

https://en.wikipedia.org/wiki/Monty_Hall_problem

That is why I spend only one dollar a week on the lottery. I know I can afford 50 bucks a year, yet the thrill of maybe winning is just as real to me as if I had spent 10 or 100 bucks.

I enjoyed Hawking's A Brief History of Time. You may have read it, if not you would probably like it.