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Here's how I'd do it.
Time until the first proc after a cooldown is a binomial distribution, with a .15 chance every N seconds, where N is your average time between casts.
The mean time until your first proc is (1/.15)*N. (Roughly, your seventh cast.)
The sequence of events will be: A proc initiates the cooldown. The cooldown finishes, and then an average of 7 casts later, it procs again. So the time between procs is (cooldown) + 7 * (mean time between casts).
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