Random event while burying banked bones?

During the initial hype following the introduction of Construction, I managed to make enough money off selling oak logs to buy the big bones I need for lvl 43 prayer. Now I built my prayer level on burying the bones of the goblins I ranged. Every time my inventory was full, I'd pause to bury the bones, and every third, fourth or fifth time I'd get a random event, and always the moment I buried the first bone of a full inventory.

I'd like to know the random event ratio for burying big bones directly from the bank. Also, does the fact that I'm burying big bones in stead of normal bones alter the amount or 'quality' of random events in any way? (As in drill demon in stead of drunken dwarf, freaky forester in stead of mysterious old man).