### Stick Broken Into Three Pieces

**Source:**http://www.cut-the-knot.org/

**Problem:**

Assume a stick is broken at random into three pieces. What is the probability that the pieces can form a triangle?

Solve it in following cases:

- Two break points are selected randomly (and distributed uniformly) on the stick.
- The stick is first broken into two pieces. The longest (or rather, not the shortest) is then broken into two.
- The stick is first broken into two pieces. A piece randomly selected with probability 1/2 is then broken into two.
- The stick is first broken into two pieces. A piece randomly selected with the probability proportional to its length is then broken into two.

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