My Birthday Paradox

Today is my birthday. So, let's celebrate by doing a math experiment. How many commenters on this video do you think it's going to take for there to be two of you with the same birthday? This is called the birthday paradox. My birthday is April 29th, so put yours, month and day, down in the comments. Although, if you want to make it random for privacy reasons, totally fine. But, do it uniformly random. You can't all choose February 29th. Now, you might anticipate this is going to be a big number, like a random person to match my April 29th, there's like a one in 365 chance that would occur. But, the number needed such that there is some match turns out to only be 23 people for it to be more likely there's a match than not. This shows you the probability distribution as you increase the number of people, and at 23 people, it tips over that 50% chance mark for the first time. It's fun to compute the probability that at least two people are going to share the same birthday. And, in probability, we often do this trick where we take one minus the probability that no two match. That's a little bit easier. So, I can write this as one minus the product of a whole bunch of factors. The first of them represents the first person. The first person's birthday can be anything. 365 choices, they can choose any of them out of the 365 options. But, for the second person, if it's not going to match, they can't choose the same thing the first person choose. It has to be a little bit different. There's now only 364 options over 365. For the third person, [clears throat] they can't match the first or second, so now we're down to 363 different possibilities. And so, you keep on doing terms like this until your number is finally over the value of a half. And that happens when you take 23 different terms. Math is so cool.