A stick has a length of units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than unit?
For the first break, the probability that you get a piece that is 1 or longer is 4/5. Then for the second break, the probability that you get a piece that is 1 or longer is 3/5. Therefore, the probability is 4/5*3/5 = 12/25.
