Help Me Settle This Argument

So I'm a dude, first off. I'm also not a martial artist, second off. Me and a friend got into an argument about a hypothetical and this is most likely one of two best places to ask in order to gain supporting arguments either for or against either of us in order to settle it. I'll explain the details and everything and I'm hoping for some answers and explanations.

The hypothetical is: A black belt BJJ trained woman and put them up against a untrained man that is twice her weight in a street fight.

My specific stance is that, although it's POSSIBLE for the woman to come out on top, it's not PROBABLE due to the sheer difference in weight and the presumable difference in raw upper body strength, height, and/or arm length. Your best bet is to avoid confrontation first and foremost because before you'd expect a proper take down where the woman would win, there's any number of scenarios that could play out where she gets struck, stumbles, shoved down first, or so on.

HIS stance is that the black belt would win more often than not because she'd control the space, get a lock, and get a take down. Basically a matter of "knowing everything that could and should happen so much that you just wouldn't ever make a mistake and you'd usually win out, even in an unregulated setting".

I'll refrain from posting my personal rebuttals to his stance because I want to keep this post as neutral as possible but I'd like to hear arguments either supporting me or him on this specific question and one of these specific answers:

If a woman of X size comes across an altercation with a man that is 2X+Y her size but untrained in BJJ, would her beating her opponent be a plausible enough outcome that she shouldn't care to just avoid the confrontation? Note that this is a street fight with no regulations.

Thanks in advance btw.