Dots on distinct edges

Three dots are placed on the edges of a square: each dot is put on one of the four edges, chosen independently and uniformly. What is the probability that the three dots lie on three distinct edges?

Show hints (2)+
  1. Each dot picks one of 44 edges independently: 434^3 assignments.
  2. Distinct edges: 4324\cdot3\cdot2 favorable.

Answer

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0.375 (± 0.001)

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Asked at: Optiver, Akuna Capital

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