Three dots, exactly one shared edge

Three dots are placed independently and uniformly at random on the perimeter of a square. What is the probability that exactly two of the dots lie on the same edge, with the third on a different edge? Give a decimal.

Show hints (2)+
  1. Only the edge each dot lands on matters - 4 equally likely edges per dot, so 43=644^3 = 64 outcomes.
  2. Pick the sharing pair (3 ways), its edge (4), and the lone dot's edge (3).

Answer

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0.5625 (± 0.005)

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