medium Probability
A release-checked medium problem for training Conditional Probability.
The surfaces of a $3 \times 3 \times 3$ cube (initially white) are painted red. The large cube is then cut up into $27$ $1 \times 1 \times 1$ small cubes. One of the small cubes is selected uniformly at random and is rolled twice. The face appearing is red both times. What is the probability the cube selected was a corner cube?
This Probability problem is tagged Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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