A ring is hanging from the ceiling by a string. Someone will cut the ring in two positions chosen uniformly at random on the circumference, and this will break the ring into two pieces. Player I gets the piece which falls to the floor, and player II gets the piece which stays attaches to the string. Whoever gets the bigger piece wins. Does either plater have a big advantage here? Explain.
Assuming the circumference has length 1, I need to find the probability that the length of the middle piece exceeds 0.5 but I don't know how to so please help me out.