A stick of length $1$ is broken at a point chosen uniformly at random. Which of the following is false?
- Twice the length of the smaller piece is greater than the length of the larger piece with positive probability.
- One half of the length of the larger piece is greater than the length of smaller piece with positive probability.
- The product of the length of the smaller piece and the larger piece is less than $1 / 4$ in expectation.
- The ratio of the length of larger piece to the smaller piece is greater than $100$ with positive probability.
- The product of the length of the smaller piece and the larger piece is greater than $1 / 4$ with positive probability.