90.Breaking the Longer Piece
★★★geometric probabilityAkuna Capital
A stick of length 1 is broken at a uniformly random point. The longer of the two pieces is then broken again at a uniformly random point along its own length. What is the probability that the three resulting pieces can form a triangle?
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Three lengths form a triangle exactly when none exceeds half the total. Condition on where the first break landed and integrate.
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