Uniform differences

What this uniform-distribution probability question tests

This is a medium-difficulty probability problem that appears frequently in quant interviews. It tests your ability to reason about joint distributions and translate a geometric constraint into a probability calculation. The setup is simple—two independent samples from a uniform distribution—but finding the answer requires you to visualize or carefully set up the region where the condition holds.

Strong candidates approach this by either sketching the sample space, recognizing it as a geometric probability problem, or working through the integral setup systematically. The question rewards clear thinking about how to measure likelihood in continuous spaces, and interviewers often follow up by asking you to generalize or modify the threshold.

• Geometric probability and the uniform distribution
• Independence and joint density functions
• Translating inequality constraints into regions