If you want to dismiss an argument, maybe do the math instead of saying "do the math" dismissively and inventing an arbitrary number without even saying across how much time that estimate is supposed to be (one in a billion, what, instantaneously? In the first hour?)
It's kind of expected here if you are going to call out someone's math to give the process you arrived to yours. Not so much a rule but expected courtesy :) "the solution is left as an exercise to the reader" is not very helpful to an argument.
