How Common is it that a Tire Blows out due to an actual faulty tire and not Bead damage from the install or some type of puncture commonly known as a Road Hazard?

Very rare. The quality controls in place at modern tire factories are such today that a defective tire is a very rare occurrence. Tire beads are very strong and it is hard to damage one to the point that is will cause a blowout. The most common cause of a blowout is an under-inflated tire especially if the vehicle is carrying a heavy load or traveling at a high rate of speed. Of course a road hazard can cause a blowout but that too is uncommon.