Riddle:

1. A point is dropped randomly on a unit segment. It divides the segment into two pieces. What is the average length of the shortest piece? The longest one? Their ratio? What is the expected value of the ratio of the lengths of the longest segment to the shortest one?

2. Two random points, chosen uniformly and independently on a unit segment, split the segment into three pieces. What is the average length of the left segment?

3. Two points are dropped randomly on a unit segment. They divide the segment into three pieces. What is the average length of the shortest piece? The longest one? Their ratio?

Python Solution:

Source:

1) https://www.cut-the-knot.org/m/Probability/RandomPointsOnSegment.shtml

2) https://mbapreponline.wordpress.com/wp-content/uploads/2013/07/fifty_challenging_problems_in__2.pdf