Well I would not say it is statistically impossible at all. But... let's say it is statistically unlikely... that it is 1 in a billion. Well... all that means is it IS likely to happen over a long period of time, right?
Plus I disagree with the randomness and chance point you make. Natural selection is actually the opposite of random chance.
"Natural selection is actually the opposite of random chance."
Then who or what selects?
"Well... all that means is it IS likely to happen over a long period of time, right?"
Why would this even happen at all?