How to calculate the probability of a 2 sigma event that happens more frequently If a two sigma event should only happen once every 44 years, what is the quantified probability of the event if it happens 3 times within 15 years?

This is a Poisson distribution problem.  An event $E$ occurs every 44 years (the two sigma just indicates what event), and it has a probability of$$P(E) = \frac {T^n e^{-T}}{n!}$$ where $T$ is the mean value of 44 years and $n$ is the number of occurrences in the time interval. The probability of 3 occurences in a 15 year interval is given by $$P = \frac {\left(\frac {15} {44}\right)^3 exp(-15/44)} {3!} = 0.004696$$
