Calculate Triangle Probability From Broken Stick
Company: ByteDance
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
A stick of length 1 is broken into three pieces by choosing two cut points independently and uniformly at random along the stick, then sorting the two cut points to form three segment lengths.
What is the probability that the three resulting pieces can form a valid triangle?
State your assumptions clearly and derive the probability.
Overview: This question evaluates a candidate's understanding of geometric probability, continuous random variables, and spatial reasoning within probabilistic models.