The Broken Clock

What this uniform-distribution probability question tests

This is an easy probability question that appears in interviews at quantitative trading firms and asset-management companies. It tests whether you can translate a geometric setup into a probability calculation, working with uniform distributions over a continuous space and measuring the relative positioning of two independent random variables.

The core skill is recognizing that you can model the problem as two uniformly random points on a circle (or equivalently, on an interval with wraparound), then computing the probability that their separation meets a given constraint. Strong solutions typically visualize the sample space, identify the favorable region explicitly, and use symmetry to simplify the geometry before computing a ratio of areas or lengths.

• Uniform distributions on a bounded interval or circle
• Independence of random variables
• Geometric probability and symmetry
• Angular distance and wraparound