Solution
The Broken Stick
Show the problem again
A stick is broken at two points chosen independently and uniformly at random. What is the probability that the three resulting pieces can form a triangle? Express your answer as a fraction.
Worked solution
The answer is 1/4. Labeling the two break points x and y on [0,1], the sample space is the unit square. The triangle inequality requires each piece to be less than 1/2 the total length. The region satisfying all three inequalities forms a triangle with area 1/4 of the unit square.
Source: The broken-stick problem, studied in geometric probability since the 19th century. Statement written for AxiomIQ.