| medium | probability |
A stick is broken into 3 parts, by choosing 2 points randomly along its length. With what probability can it form a triangle?
All three broken parts must satisfy the triangle inequality. Or rather, each of the broken part must be less than half of stick's length.
1/4
All 3 sides have to have lengths less than half the length of the stick. the conditions are min{ x.y}<= 0.5; max{x,y}>=0.5; |x-y|<=0.5 . looking at the unit square, and dividing into 8 congruent triangles by lines parallel to the axes and y=x line, its easy to see 2 of the 8 triangles satisfy the condition. so the answer is 1/4