A cube painted red on all sides is cut into 125 equal small cubes. A small cube when picked is found to show red color on one of its faces. The probability that two more faces also show red color is :
Step-by-Step Solution
Key Concept: Use conditional probability P(3 red faces | at least 1 red face) = (number of corner cubes with 3 red faces) / (total cubes with ≥1 red face). A 5×5×5 cube has 8 corner cubes (3 faces painted), 36 edge cubes (2 faces painted), 54 face cubes (1 face painted), and 27 interior unpainted cubes.
This is conditional probability. Total cases with at least one red cube: $125 - 27 = 98$. Among these, cubes painted on exactly three sides: 8. The conditional probability is $ rac{8}{98} = rac{4}{49}$.
Correct Answer: 2