A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ 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.
