A stick is randomly broken into 3 pieces . Determine the probability that the sum of the lengths of any 2 pieces is greater than the length of the third piece.
Geometric solution (non-strict): let $x$, $y$ and $z$ be lengths of pieces. Then in space with $xyz$ axes you have a triangle ($x+y+z=L, x\ge 0, y\ge 0, z \ge 0$). Total area of triangle corresponds to probability 1. Subsets of fitting pieces also correspond to a triangle, with area $1/4$ of the original one.