Will the three-legged table stand?
A round tabletop is a disk, and three legs are attached at points chosen independently and uniformly on its circular edge. The table stands (doesn't tip) exactly when the disk's center lies inside the triangle formed by the three leg points. What is the probability the table stands?
Show hints (2)+
- The center is inside the triangle iff the three points do NOT all lie in a single semicircle.
- For a fixed point to be the clockwise anchor, the other two must fall in its semicircle: probability . Three disjoint anchors give for "all in a semicircle".
Answer
Reveal answer →Final answer
0.25
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Asked at: Jane Street, Optiver