Beside the Point
A Jane Street geometric-probability puzzle: two random points (red and blue) are drawn uniformly from a unit square. What is the probability that there is a point on the blue-nearest side of the square equidistant from both?
For the condition to hold, the perpendicular bisector of the two points must cross the blue-nearest side of the square. A Monte Carlo simulation over a million trials gives approximately 0.4917, slightly under half. Full geometry and Python code in the PDF.