I want to teach a short course in probability and I'm looking for some counterintuitive examples for it. Results that seems to be obviously false but they true or vice versa... I already found some

"Do the same math as we did above with the floodplains, in precisely the same way, and we see a 37% chance that any American of average life expectancy will experience at least one nationwide violent revolution." By BJ Campbell.

Are some scientific results so unexpected that we should just reject them?