A line segment is broken at two random points along its length. What is the probability that the three new segments can be arranged to form a triangle?
+600 I like this one. Let the sides be $x,y,1-(x+y)$. By the triangle inequality, all of the following must be true:
$$x<1-x$$
$$y<1-y$$
$$1<2x+2y$$
Graph each of these on the coordinate plane and use the principle of geometric probability. It's $\frac14$.
