What if I told you there’s a fifty percent chance that 2 out of 23 people have the same birthday?


I know, these first few cards have nothing to do with birthdays, but it’ll get there.



Let’s change gears.



This is the last part.



To answer some questions people have asked me after I showed them my index cards:
1) No, I certainly did not come up with this myself. I proved exactly 0% of this whole thing. If you see something wrong with the math, you can either tell me in the comments (I actually might be able to respond after having to defend it so many times) or look at some other websites that explain it in a more mathematical (AKA complicated and confusing) way.
2) No, I do not have too much free time. I have a perfect amount, thank you very much.

The story behind this post: I first heard about the birthday paradox/birthday problem on a podcast last year, and I immediately told my dad about it. He didn’t believe it at all, which was very true to form for him. Even though I didn’t really get how it worked, I thought it was interesting and wrote it down as a blog post idea. It’s title at the time was going to be Weird math things.

Then two weeks ago, I looked through my idea list and decided: hey, it’s time for this birthday paradox thing idea to shine. I researched the math behind the whole thing and created a series of index cards explaining it. My guinea pigs were my parents. It was pretty funny. The next day, I brought it to school. My friends were both confused and amused by it.

On Sunday, I brought it to church, which was where I’ve gotten my best reaction so far. At the end of a demonstration, the first guy said oh, that’s pretty cool and the second guy agreed. Then the first guy showed me his digital drawing of a super cute Squirtle (it’s a Pokemon) that he did for school and the second guy made a insightful suggestion that I would’ve have never thought of.

You know that card that says “If you’re skeptical, count them all. I’ll also prove them?” Before, it said, “If you’re skeptical, don’t count them all. I’ll prove it.” He said that didn’t make sense because someone who’s skeptical would want to count them all.

The other cards have also gone through transformations. The cards you saw is an improved version. The first series looked pretty different, but along the way, I asked for feedback and suggestions to make it less confusing. At first, the cards started out by asking, “How many pairs can be made with three people?” The word “pairs” was confusing, and people thought the answer was just one.


What do you think about this birthday paradox thing? Do you know of any other weird math things? Oh! Here’s one: that .9 repeating equals one. And feedback! Were there any cards that were confusing and what would make them more clear?


8 thoughts on “What if I told you there’s a fifty percent chance that 2 out of 23 people have the same birthday?”

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