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What are the odds?

Somebody here will be able to give a mathematical answer.

The Verizon representative I just spoke to informed me it’s her birthday and it’s my birthday too. (Isn’t there a song?)
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That would be roughly 1 in 133,225. Not really a miracle, but quite rare. And happy birthday!
@NerdyPotato Are you assuming same birth year? Because I'm not sure that's the case here.
@ElwoodBlues no, just a 1 in 365 chance that someone shares the same birthday and a 1 in 365 chance the contact takes place on that day.
@NerdyPotato Got it; now I see what you did. Might need to multiply by the average number of contacts per day.
@ElwoodBlues it should be divided by that indeed, but that's difficult to estimate. And it should be multiplied again by the chance that someone doesn't mention their birthday to be even more accurate.