Red faces on a diced cube

A 10×10×1010 \times 10 \times 10 cube is painted red on all outer surfaces, then cut into 10001000 unit cubes. One unit cube is chosen uniformly at random. What is the expected number of red faces it has?

Show hints (2)+
  1. Total painted unit-faces = surface area of the big cube =6102=600= 6\cdot 10^2 = 600.
  2. Divide by the 10001000 unit cubes.

Answer

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0.6

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Asked at: Jane Street, Optiver

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