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That would be insanely improbable.
For example, out of any 23 people, there is a 50% chance that two will share the same birthday.
For zero coincidences to ever occur would be mathematically impossible.
Do you understand your statistical analysis error?
Why is it a coincidence for people to share the same birthday? It's not a coincidence at all; birthdays relate to conception dates; people having sex has to do with external factors that often compel sex to be had in batches - for example, the holidays being a common conception date.
Coincidence doesn't JUST mean things matching, it means things matching in a way that defies the odds or factors in place. If everyone born in a certain year had the same exact birthday, and there were no external explanation, that would be a massive coincidence. If there were an external explanation, it isn't a coincidence.
Colloquially coincidence can refer to something matching up in a visible way with factors that cause it being unknown (and not really cared about) by the observer; like if a bird died and hit you in the head whilst you were walking along. There's factors that explain that happening, but the observer likely won't know or care about those factors, and can dismiss it as a "coincidence".