断棍成三角形：两次随机断与先断再断长段
Given a stick
题目详情
You are given a stick of unit length.
(i) The stick drops and breaks at two places. What is the probability that the three pieces could form a triangle?
(ii) The stick drops and breaks at one place. Then the larger piece is taken and dropped again, breaking at one place. What is the probability that the three pieces could form a triangle?
解析
(i) 经典结果：两点独立均匀随机断三段，能成三角形当且仅当三段都小于 ，概率为
(ii) 先随机断一次，取长段再随机断一次。最终三段能成三角形的概率为