Humans are bad at statistics and probability. We're naturally wired to find patterns and connections and make decisions quickly without needing to perform calculations. It works for simple stuff but when things get a little complicated our "gut feeling" tends to be wrong.

My other favourite probability paradox is the Monty Hall Problem. You're given the option to pick from 3 doors. Behind 2 of them are goats and behind 1 is a new car. You pick door #1. You're asked if you're sure or if you'd rather switch doors. Whether you stay or switch makes no difference. You have a 33% chance of winning either way. Then you're told that behind door #2 there is a goat. Do you stay with door #1 or switch to door #3? Switching to door #3 improves your odds of winning to 66%. It's a classic example of how additional information can be used to recalculate odds and it's how things like card counting work.