(1) If a unit length segment is randomly broken at two points along its length, what is the probability that the three pieces created in this fashion will form a triangle? ("Random" here means that the location of each break point is uniform on the unit interval.)
(2) If the unit-length segment is broken at a random point, and then one of the two pieces is randomly selected (not necessarily equally likely) and broken at a random point on its length, what is the probability that the three pieces will form a triangle?
(3) If the unit-length segment is broken at a random point, and the longer of the two pieces is then selected and broken at a random point on its length, what is the probability that the three pieces will form a triangle?
(4) Suppose that three unit-length segments are each broken at three random points chosen independently, and one of the two pieces from each is taken. What is the probability that the three pieces will form a triangle?