Simple Explanation of the Birthday Paradox

How many people need to be in a room for it to be more likely than not that at least two of them have the same birthday? The surprisingly small answer to this question is what's often dubbed "The Birthday Paradox". With only 23 people being necessary, we'll discuss why this is, look at the math, and a simple reframe of the numbers. #maths #mathematics #paradox

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[WrathofMath]

Please ignore my inclusion of the /yy early in the video, we aren't considering year - only day and month. Professional silly goose over here.

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[arthurmatthewf]

When I taught this to my statistics class I demonstrated it by going around the room and asking every person's birthday. Usually it worked with 35 students, but when it didn't, no matter what the last person said, I responded "OMG, that's my birthday too!!!" They never caught on. LOL

[trevorfultz]

I’ll never forget when we tried this in practice in one of my Statistics courses and legit person 22 and 23 shared the same birthday. They were sitting next to each other and did not know beforehand.

[gpcm]

I love when mathematicians can explain their concepts with simple logic

[Xtianzzyzx]

I'm not a math guy, and I have no idea why I clicked this video while lying in bed with a fever. But this was dope haha

[bsimp]

I worked in an office with exactly 23 people, and we did indeed have two people who shared the same birthday. I screamed BIRTHDAY PARADOX when I found out.

[BenGoodbrand]

The dd/mm/yy from an American gave me more joy than I ever thought possible.

[kaptainkarrottop]

You had me up until 1:20 then my mind switched to a giant snowman head and a baby penguin cry.

[jonnomonodesu]

You included 'yy' in the example so the calculation would be completely different as you would have to include the odds of the year being the same which changes the problem. The video only covers the dd/mm calculation.

[DP-ugoh]

0:23 I stopped watching because the “not very likely” wasn’t aligned with the circle.

[RobbieGoodwinSY]

Brilliant. Thank you so much.

I've seen a dozen 'simple explanations…' of the birthday paradox, all of which left my head spinning.

This one really is simple, and actually works.

[lindakay]

Dude. I BARELY passed pre-algebra. I dropped out of school before Algebra. But you made this so easy and FUN to understand, I'm totally hooked, and want more! ❤❤❤

[rosebuster]

One reason that I think people are so surprised by this result is because it's in our nature to be focused on ourselves and they misinterpret what this birthday paradox is really telling us. A person might think: no way, I've been through various schools and every time our class was about 30 people and I never shared birthday with any of them. But he doesn't realize that nobody said he's going to be the one sharing birthday with somebody else in the group. There may be more than 50% chance that there's a pair of people in that class that share birthday, but it's still unlikely he is a part of that pair. More likely it's gonna be some of his classmates instead.

[itzfuture]

Best explanation of this I have seen, seeing the connections drawn made it click.

[jaygee]

I noticed that at 0:46, you wrote the date as dd/mm/yy. The way the world knows it to be.

[berzley]

The music really brings out some nostalgic memories.

[thatoneginger]

When you said 23 factors you weren’t totally wrong; it’s just the first factor is the probability that the first guy doesn’t share a birthday with anyone previous, which is 365/365, or 1

[LaurierLachance]

No idea how i ended up here but that was so cool! And thanks for that nintendo music 🔥

[MrPOKER]

I'm sorry, but I couldn't listen past 1:30. Beyond that, all I heard was the penguin's scream.

[clifhaley]

Odds are 100% that no one in any room you occupy has such killer penmanship.