## probability puzzles

medium | probability |

The stick drops and breaks at a random point distributed uniformly across the length. What is the expected length of the smaller part?

The probability that the break point belongs to first half is 1/2. In this case, the expected length of the small part is L/4. Its L/4 in the other case too. Hence E = 1/2 * L/4 + 1/2 * L/4 = L/4