Suppose that X1, X2, X3 are independent U (0, 1)-distributed random variables and let (X(1), X(2), X(3)) be the corresponding order statistic. Com- pute P (X(1) + X(2) > X(3)).
Remark. A concrete example runs as follows: Take 3 sticks of length 1, break each of them uniformly at random, and pick one of the pieces from each stick. Find the probability that the 3 chosen pieces can be constructed into a triangle.