Let's simplify the problem a little, and assume there's only three swings in the fight, they happen 8 seconds apart, and each swing has a 1/12 chance of a proc.
Using Y for a proc and N for no proc, there's 2^3 or eight possible outcomes:
YYY
YYN
YNY
YNN
NYY
NYN
NNY
NNN
In each of these eight outcomes, how much total damage does the proc do?
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