# Thrice in a Blue Moon

On the planet Blue Ox, there are three moons: a red one, a blue one, and a regular one. The red moon orbits around the planet once every 66 days, the blue moon orbits around the planet every 3 days, and the regular moon orbits around the planet every 30 days. The inhabitants of Blue Ox love to throw pies at newcomers. They would usually throw their pies at the newcomer unless that the day is when their three moons line up in a row, because they think that day is unlucky. Josh the Astronaut has just arrived on Blue Ox. The probability that he would be hit with pies is a fraction \(\frac{a}{b}\). What is a+b?