I'm stuck with a question: Two points are selected at random on a straight line segment of length 1. What is the probability that a triangle can be constructed from the results line segments.
So far all I can come up with is:
- Points p1 and p2 have equal probability of 1.
- Lengths a, b and c can be formed from two cases; if p2 > p1 then a = p1, b = p2 - p1 and c = 1 - p2. For the other case, p1 and p2 are reversed.
- The inequality must be satisfied. I can substitute p1 and p2 in, and imagine some double integral over p1 and p2 for each case, but I don't know how to deal with the inequality.