By the book answer:
Double personal foul (4-14-f BR 48): two opponents commit fouls against each other at approximately the same time.
Before the release (assumption that ball hasn't left the hand since you've used the word AS), basket does not count.
Possesion goes to team that previously had player or team control (NCAA 10-12-summary BR-87). New rule this year rather than going to the AP arrow.
Real life answer:
I would hope that one official would acquiesce (likely the trail to the Lead) and "determine" that one "occurred" before the other.
However, the scenario where I see this likely happening is where airborne shooter A1 uses free hand to clear space, while B1, who doesn't have legal guarding position, slides under A1.
Ugly crash, but both fouls require calling.
Tough situation. I've heard that Charles Range made this call in a D1 game a few years back, on TV no less, but I didn't see it myself.
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