Statistics aren't reflective. They're aggregate. It's not a 50% chance of being on the date you chose, but that any two dates are the same. If you pick a rand

Statistics aren't reflective. They're aggregate. It's not a 50% chance of being on the date you chose, but that any two dates are the same. If you pick a random date, Alice has a 364/365 chance of not having a birthday that day. Bob has a 363/365 chance of not having a birthday on that day or on Alice's birthday independently of whether or not Alice's birthday is on the random date. So we take Alice's chances and Bob's chances and we can multiply them together to get our odds that none of these people share a date. And of course, if we know the odds of something not happening, the odds of it happening is the opposite.