Probability of picking 2 numbers between 0 and 1 to be within 1/2 distance of each other?
What's the probability of picking 2 numbers, x and y, between 0 and 1 such that they will be within the distance of 12 of each other?
In other words,
I solved the problem through a geometric approach by rewriting the probability as
From the graph, I calculated the red area to be 75%.
Question: What would be a non-geometric solution to this problem?