Break the Longer Piece
A stick of length 1 is broken at a point chosen uniformly at random. The longer of the two pieces is then broken at a point chosen uniformly at random along its length. What is the probability that the three resulting pieces can form a triangle? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
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- A Product Below One Half 5.0/10
- Square Beats Product 5.0/10
- The Broken Stick 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.