Given that the full moon occurs every 29.5 days what is the long term probability that when a blue moon occurs it is in a specific month? Use the regular (every 4th year) leap year formula for February.

Consider a world/calendar with a lunar cycle of exactly 29 days and whose months are randomly assigned 30 or 31 days (with equal probability and no yearly repetition.) What is the long term probability that a blue moon falls on a 30 day month?