Ten dice, sum divisible by six

You roll ten fair $6$ -sided dice and add the results. What is the probability that the total is divisible by $6$ ?

Show hints (2)+

A fair die is uniform over residues mod $6$ .
Fix nine dice; the tenth cycles the total through all six residues equally - so each residue has probability $1/6$ .

Answer

Reveal answer →

0.1667 (± 0.001)

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