Question

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

Answer 1

Answer:

The stick drops and breaks at a random point distributed uniformly across the length. What is the expected length of the smaller part 0.25

Answer 2

Answer:

0.25

Explanation:

With probability 1/2 each the break takes place in the left half, resp. in the right half of the rod. In both cases the average length of the smaller piece is 1/4. Therefore the overall expected length of the smaller piece is 1/4.

Another Explanation:

The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit, which is answer