Assume the endpoints of the stick are at the points 0 and 1.
Let and be the two breaking points, chosen at random from the values in the interval .
Let us assume at first that . The three sides of the triangle have lengths , , and . The three conditions that must be satisfied for a triangle to be formed are thus:
Simplifying these inequalities gives us:
, , and .
We can rearrange this to give:
The total probability for this case can thus be given by the integral:
Considering that the other case (that ) is equally likely, the total probability that a triangle can be formed is .