Sum of ten dice being a multiple of six

Question

Ten fair six-sided dice are thrown and their faces are added. What is the probability the total is a multiple of $6$ ?

Short answer

$1/6$ . Condition on the first nine dice, whose total is some $x$ . The last die makes the sum one of $x+1,\dots,x+6$ with equal chance, and exactly one of six consecutive integers is divisible by $6$ .

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Lessons behind this question

Counting and Combinatorics
Expectation, Mean, and Variance
Sample Spaces, Events, and the Probability Axioms

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