This was a good overview of what’s possible with statistics: Statistician Answers Stats Questions From Twitter | Tech Support | WIRED.

But I’m pretty sure that at t=11:23 he gets it wrong. The probability that three people in a family have the same birthday isn’t 1 * 1/365 * 1/365. but rather it depends on the number of people in the family (starting, I guess, at some epoch). This is known as the Birthday paradox.

To be clear: they’re not asking what is the probability of three people being born on January 10. They asked what are the odds of three people from an unspecified family size being born on the same day (could be any day of the year).