A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 2 units?

If all three resulting pieces are shorter than 2 units, then the sum of the 3 pieces would be less than six, the length of our big stick. Therefore, there are no ways to make 3 pieces shorter than 2 units, so the probability is 0.