444.The Twice-Red Painted Cube
★★★conditional probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
A white cube is painted red on its outer surface, then cut into 27 unit cubes. One unit cube is selected uniformly at random and rolled twice; both rolls show a red face. What is the probability the selected cube is a corner cube?
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Corner, edge, face, and center cubes have 3, 2, 1, 0 red faces. Apply Bayes with squared likelihoods.
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