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Medium · Market Microstructure · Quant Trader interview question · logic, probability, combinatorics
You have two cubes used to represent the days of the month (01 to 31). Cube 1 has faces: 0, 1, 2, 3, 4, 5. Cube 2 has faces: 0, 1, 2, 6, 7, 8. The digit '6' can be used as a '9'. Assuming each arrangement of the two cubes is equally likely, what is the probability that you can form a valid date representing a day of the month? Note: leading zeros are permissible (e.g., 01, 02, etc.) and '6' can represent '9' when needed.