We have a metal rod of length L. The rod is on the x-axis extending from...

We have a metal rod of length L. The rod is on the x-axis extending from 0 to L. We select a point X on the rod randomly and uniformly and cut the rod at X. This gives two smaller rods of lengths X and L − X. We select the longer piece (if the two pieces are of equal length we select one of them) and cut it again randomly and uniformly to get three pieces. What is the probability that we can form a triangle with the three pieces? (Hint: From basic geometry, a triangle with sides of length a, b, and c exists if and only if a < b + c, b < a + c, and c < a + b; i.e., if the triangle inequality holds. )

Expert Solution

Thus, total probability is -

orchestra answered 2 years ago

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