We have the unit interval $[0,1]$ and we want to find the probability of picking two random numbers $a,b$ from that interval with $|a-b|>0.5$.
Must I investigate $[0,1]×[0,1]$?
I don't have the faintest idea of how to solve this. The problem is that $[0,1]$ has infinite numbers to pick from… so how to calculate a probability with infinitely many items in the sample space?
I would be really happy if somebody shed a light on this.