Probabilities on the analogue clock

In how much % of the time of a day are all three hands of an analogue watch located in the right half of the dial? First of all, the hour hand is located on the right side of the dial in 12 of 24 hours (50%). Of this time, the minute hand is located on the right side in 6 of 12 hours (25%). Of these 6 hours, the second hand spends 3 hours on the right side (12.5%).


This intuitive explanation can also be easily proven:

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The probability applies not only to the right half of the dial, but to any half.

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