Considering mining as a ‘process in which events occur continuously and independently at a constant average rate,’ I found this article https://en.wikipedia.org/wiki/Exponential_distribution and used it as a reference.  It gave me ready to use formulas for the probability distribution that describes the time between events in such a process.  The cumulative distribution function 1 - e^-λx is the probability of encountering an interval shorter than x, where

• λ = 1/β is the rate, and
• β = 10 minutes, i.e. the mean time between events.

The likelihood of an interval longer than x is then e^-x/β.  For instance, intervals longer than 5 times the mean time happen with the probability of e^-5.