I note the math observations with some discomfort. After all, its the thrust of the thing we are pursuing, not the absolute scientific truth. Consider this; What if there are other, as yet unidentified assigned goons? I urge you to ponder deeply before loosing the smallest metaphoric member we possess, thus inspiring a forest fire, the likes of which we may never yet have witnessed!
The PHB can't do maths. If they each had a .5 chance of success, between them they have a 0.75 chance. If they have 0.33 and there's three of them, the odds of success drop to 0.699237.