Let a, b be real numbers randomly selected independently and uniformly from the range of (0,1).
What is P(a < b)?
The problem here is that a can be equal to b, so is P(a < b) ≈ 0.5 or P(a < b) → 0.5 formally correct? Or anything else?
What I'm looking for here is a correct formal way to write this probability down.