Simple Explanation of the Birthday Paradox

[@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. More math chats: kzbin.info/aero/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Join Wrath of Math to get early&exclusive videos, lecture notes, music, and more! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin

[@gigeo48]

That's what I was thinking. there's a better chance of people sharing birthdays only considering day and month than people sharing day, month and year.

[@seyfehdaie1156]

I enjoyed it so much. Very interesting. Thank you. Seyf Ehdaie

[@darrellbanks924]

Why is this a paradox?

[@vincentkingsdale8334]

I am glad you said that bc if you included the year the probability would reduce significantly

[@RCFrizz]

I noticed that immediately, and wondered why you didn't catch it. If you had any self-respect, you would have corrected it.

[@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.

[@arthurmatthewf5406]

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

[@EricDanzeisen]

Hahaha.

[@mikeblake9761]

Statistical dictatorship 😂 the stats have no choice but to stat

[@Chishannicon]

You demonstrated it by lying to make it true more often than it actually was?

[@arthurmatthewf5406]

@@Chishannicon I made it a fun lesson. Naturally, after I taught the math in the following class I fessed up. I had standing room only statistics classes because I was so much fun.

[@jaymay7957]

@@Chishanniconmakes ya wonder if you can believe anything they claim is true

[@gpcm]

I love when mathematicians can explain their concepts with simple logic

[@raybaxter4683]

@@undergroundmoe See the above video for an example.

[@YHWH-XY]

Sadly it wasn't this video, it could've been explained so much simpler but he had to stretch it to 12min for ads. Repeated the same stuff like 10^23 times

[@alansun70]

More possible pairs. 23 is the number of chromosome pairs humans have. It's the 9th prime number & the smallest prime that isn't a twin. 2 & 3 digit primes are easy to memorize. 4 digits are hard & hard to mentally break down.

[@bsimp07]

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.

[@chenilleoneil1289]

Did anyone understand?

[@LucasDanielSantoro]

I choose to believe the all 23 people found out at the same time and the 21 not sharing birthday screamed in unison BIRTHDAY PARADOX

[@BenGoodbrand]

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

[@Bhuwan_Bansal]

Indeed😂

[@christopherbedford9897]

Canadian! He gives himself a way a couple of times with with "aboat" 😝

[@0356danmcc]

@@christopherbedford9897 Agreed! He's a Canuck :)

[@anon_y_mousse]

Both the US and UK date formats are wrong. You don't tell someone the time of day by listing the seconds then minutes then hours. The international format of YYYY-MM-DD should be the format that we all use.

[@BenGoodbrand]

@anon_y_mousse were talking date, not time.

[@kaptainkarrottop5372]

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.

[@WrathofMath]

very silly oversight! Thankfully we didn't spend too much time with the mm/dd/yy, so hopefully it won't cause confusion

[@sdspivey]

The bigger problems are, It should be YYYY (4 digits) and should be in the format YYYY-MM-DD, as specified in ISO 8601:2000. It has been over 2 decades, learn to write your dates correctly.

[@Vampire-Catgirl]

​@@Mikemenn If birthday only means the full date of your birth, including year, then what do people say to you on your birthday, or what do you say to people on their birthday? You can't just say "happy birthday", because according to you that includes the year, but it's not the year of their birth, it's only the month and day Do you say "Happy celebration of your birthday", or maybe "happy birthday anniversary"?

[@Vampire-Catgirl]

@@Mikemenn Replying to my question with a yawning emoji doesn't make you look cool like you think it does. It makes you look disrespectful and rude. Congratulations.

[@Vampire-Catgirl]

@@Mikemenn Well I'm sorry, I didn't realize that you don't like answering simple questions or talking to people. It won't happen again.

[@genesisflix]

If you’re thinking, “so if there were 22 other people in my room, one of them should have my birthday?” That’s why it doesn’t make sense to you. It’s not personal. It’s “there’s a 51% possibility that two of all these people, in any combination, share a birthday.” That makes it sound more plausible.

[@FlicksForever]

Nope.still not.everybody write their birthday on the chalkboard. There is 23 birthdays on the board. Doesnt matter how many combinations there is between people. Every one of those 23people will look at the 23 birthdays written on the board and no one will have the same birthday.atleast most of the times it is atempted

[@genesisflix]

@@FlicksForever right but you’re thinking “likely” instead of “more likely.” The idea is not that it’s extremely likely, just more likely than not. Here’s why the math actually works. You’re comparing each birthday to each of the other 22 birthdays. So YOU personally get 22 chances to match a birthday. Then the NEXT person gets 22 chances. With 23 people that’s (23x22)/2=253 pairs of possibilities. There’s 365/366 days in a year, so 253 days/pairs is more than half of the year, which is why it’s mathematically true. But just because it’s mathematically true, that doesn’t mean it will happen, just that out of 100 trials, it’s likely that more than half will have at least one pair that matches.

[@FlicksForever]

@genesisflix im just saying.that in the end there is just 23 birthdays no mater how many combinations there is between people. 23 people, 23 birthdays.write it on the whiteboard and then see if there is 2 of the same. Most of the time non will be the same. I understand the math perfecly. But in this situation the math is irelevant.

[@genesisflix]

@@FlicksForever I get what you’re saying. It’s everyone writing their birthday on the board, and trying to find a pair. 23 doesn’t feel like enough. The math also says that if you have 75 people, it’s 99.9% that two people share a birthday. None of it seems logical, but that’s why it’s an interesting thought experiment.

[@opus5770]

​@@FlicksForever the math is never irrelevant when we're talking about probabilities. You don't understand it, and you're working on assumptions only.

[@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.

[@Chris-c7i8d]

Yes indeed. Outside of mathematics fans, most people hear this question as - How many people do you need before someone has the same birthday as you?

[@georgkrahl56]

@@Chris-c7i8d : Theoretically an infinite number of people.

[@spongbong0]

explain ​@@georgkrahl56

[@GaboH-h7s]

Nah, in every school and every job I had the school/workplace had a calendar with our birthdays, that without mentioning FB which tells you everyone's birthday. I can say with great certainty I never shared birthdays with anyone, I know a few people I share birthday with but they are acquaintances at parties or something. I think the fact that this doesn't work for some people is because in some dates more people are born than others.

[@AVR0709]

Ironically, I studied in three different schools since elementary school and I had at least one classmate in each of the schools who shared their birthday with me. Also the fact that I have a twin sister is more fascinating to those classmates because they are literally sharing a birthday with a pair of boy-girl twins. Now what's even crazier is that the classmate from the first school of the three I mentioned, later joined the same third school as me. The world just feels a tad bit smaller each time I think of this.

[@se7sTC]

The core of the paradox is that in the initial example, we were looking for the likelihood of another person sharing the same birthday as the first person, which significantly would have reduced the number of pairs in the question (down to 22) if we operate under the same assumption. The question wording changed from fixating one person in the pair to “any two persons” in the group, hence the much larger number of pairs

[@thesolaraquarium]

exactly. not a paradox at all in my mind. You only need one pair and you have lots of people. The first example, just two people was way harder, much less probable.

[@midgetwars1]

@@thesolaraquarium Yep. When most people think of this, they'd go there's 50 people share the same birthday? But what they're thinking is sharing of the same birthday as themselves. Which yes, in that case it would be 1/365 chance.

[@dataandcolours]

Yes. That is an excellent point. That is why we should never start with an example of just 2 individuals because that increases the risk of student misunderstanding the actual scenario into the classic mistake of just thinking about anyone sharing YOUR birthday (no matter how many times you later on say anyone shares a birthday). But the sad thing is that many, for some reason, wants paradoxes to appear stronger than they actually are. This subconsciously make some people be sloppy when doing the initial explanation.

[@IvanToshkov]

Once at a party some lady was explaining how certain dates seem to be "special," because important events happened on them. I told them about this paradox and showed that just 23 events will be enough to make it more likely to have such collisions. And it's not that hard to come up with important events. I haven't been asked on such parties since.

[@mattsadventureswithart5764]

Using maths or facts to show that superstitious stuff is nonsense appears to upset people. I have no idea why.

[@IvanToshkov]

@@mattsadventureswithart5764 It's bad luck, that why! :D

[@bryn.1tbs]

​@@IvanToshkov ​@mattsadventureswithart5764 You'll both get an invitation to the next party I throw.

[@mondotv4216]

Reminds of the Mitchell and Webb sketch about the brain surgeon and the rocket scientist.

[@2011Cape]

Underrated space use 😂💯

[@1BlueEyeCreativeStudio]

In my family, we've had several sets of people that shared a birthday. My great grandparents shared a birthday (and 1 of them was a twin, so, 3 names on that cake!). A sibling and a cousin share a day. And my dad shares his birthday with my mom's sister-in-law, and 1 of my husband's uncles. I've met 2 people who share my birthday, no one in my family, though.

[@itzfuture5239]

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

[@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

[@WrathofMath]

Yeah, I only put the correction because in the video I was specifically discussing factors less than 1. A minor slip of the tongue!

[@climatebell]

I absolutely loved this video. It was very counterintuitive but also very easy to understand when you explained it.

[@davidhood4776]

I work in a group of 15 total people. The birthday coincidences in that small group are staggering. I share a birthday with one man (Jan 5), one man shares my brother's (doesn't work with us, just tied to me) birthday (Sept 5), and another man is one day younger than me and born in the same hospital so we were in the hospital nursery together, but met 54 years later. I think the system had a glitch when it put us all together.

[@bartz4439]

Throughout entire educational system and having 30 kids in class never had 1 class with two having birthday on same day. That's must be really rare

[@matthewmaning4859]

In elementary school I shared a birthday with a classmate. In highschool I shared a birthday with my sophomore history teacher and my junior year shared a birthday with 2 classmates in my science class.

[@doomofthedestiny8065]

I'd vaguely heard of the paradox before, but as soon as he clarified its ANY two in the room share a birthday it totally made sense to me because it's no longer just a series of 1/356, we get some addition as well. Edit: I realize I phrased that poorly... but I can't think of a better way to say it without just recapping the video, lol.. in short, his method of basically subtracting instead is simpler mathematically, but conceptualizing it as a positive is good enough to break the notion of it being a so-called paradox.

[@Szejski]

I understood what you meant right away, maybe because I feel the same way. I thought it was about the situation where an invited person has the same birthday as the host: that would be weird. But if any 2 people in a room/house/whatever may have the same birthday, then to me it doesn't conflict with common sense.

[@colinsmith2005]

I sold cars for ten years so noted every purchasers birthday on docs, I had one who’s birthday matched mine, correct year. He was the only person I’ve met with my birthday, ever, I was so surprised, he didn’t seem to care.

[@Leoncroi]

I'm a guy; I grew up with a lady that had my exact birthday. I always found it humorous that when I went to the hospital and gave my DoB, their first question was always are you "Rachel?" My last name is even alphabetically before hers, how do you fail an obvious 50/50?

[@asdbanz316]

how many of them purchased a car close to their bday?

[@stevewindisch2882]

I had a similar experience when I worked at a grocery store and they made us ID every single alcohol sale. I was like "Oh, cool! We were born on the same exact day!" And she was completely nonplused

[@MrDifsh]

If I went to buy a car and the guy told me he had the same birthday as me I wouldn't care either.

[@modernemily8606]

I had an assistant manager who would sometimes say things like, "I'm no spring chicken," or, "I'm older than you think I am." So I finally asked her how old she was. Turned out we were both 27, and would be turning 28 in the same month... and on the same day. We had the exact same birthdate. I told her she needed to stop complaining about how old she was.

[@stuartofblyth]

Many years ago I had a class of 18 students and decided to try this anyway. It worked. Leap year babies have two birthdays - either February 28th OR March 1st in an ordinary year and 29th February in a bissextile year.

[@johnpcheramie]

The reason that this problem is so confusing is because most people misunderstand the premise. Even though you hear " what are the odds T two people would share a birthday", for some reason your brain says " what are the odds someone would share A specific birthday" which is a completely different question. But for some reason our brains shortcut to it

[@gwilson314]

speak for yourself. it's clear that adding more and more people increases the number of days that can be shared in a year.

[@johnpcheramie]

@gwilson314 bro do you even read my comment. Like Jesus. I said the people who were confused. Then you went on to explain that you're not confused. So clearly my comment wasn't about you. And if you were confused over my comment, I highly doubt you've understood the context of this video

[@gwilson314]

@@johnpcheramie Your comment indicated that there was some defect in "our brains" which makes estimating probabilities unintuitive, I pointed out that this is nonsense by highlighting a simple heuristic as to how to approach understanding the "paradox." It is you with the learning disability, not mankind in general.

[@johnpcheramie]

@gwilson314 I genuinely think maybe you have reading comprehension issues. Please try again.

[@macman975]

​@@johnpcheramieYou really felt the need to write a second comment just to carry on insulting someone?!

[@clifhaley5150]

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

[@phillbr51]

I don't know why this is called a paradox, it's really not, it's just one of the many examples in probabilities that people's assumption about it wrong. That's simply because people think of it in terms of "What's the likelihood someone has the same birthday as one person in particular".

[@holoduke51a]

That's why its called a paradox.

[@phillbr51]

@@holoduke51a paradox doesn't mean "thing most people have wrong assumptions about". Paradox is something science doesn't have a definitive explanation for. This is something quite easily explained with undergrad mathematics.

[@Im_Ish]

That's why he specifically called it a verdical paradox. Something that sounds wrong but is true. So kinda like an optical illusion of logic. I guess your argument could be that verdical paradoxes do not exist and the way people feel about them is meaningless in regards to logic.

[@Phobos_Anomaly]

​@@phillbr51 As he said, it's a veridical paradox - like the Monty Hall problem.

[@justinbrinkworth4721]

This is explained specifically in the video.

[@GlobalWarmingSkeptic]

I remember doing this test in class when I was in 4th or 5th grade and everyone was astonished that most of the time two would share a birthday. It was baffling but as I got into computer science I started to understand how these small probabilities can explode very quickly when you're talking about networking nodes or finding matching features of a dataset. It really is astonishing.

[@jaknap1]

Forget about someone in the room having same birthday. I have lived 57 years and I have yet to meet someone that shares my birthday.

[@Potemkin2000]

Feb 30?

[@okedoke1234]

Feb 29

[@theLilaQ]

@@Potemkin2000what kind of calendar are you using?

[@2011Cape]

This is sarcasm, I assume? We don’t ask everyone we meet, “What’s your birthday?” 😆

[@adamkormendi5904]

But this is not the same problem presented here! He did not say that there should be 23 people in the room to likely share birthday with YOU, but that any random two (so you might not be involved).

[@LaurierLachance]

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

[@NoNowwwell]

Nice Mario 64 penguin world music.

[@Mark-db1ok]

Here's a fun math fact: I hate math, yet I sat through this entire video. Well done, sir 👍🏼

[@xyzxyzxyzxyzxyzxyz]

And in Scandinavian countries, where children are typically born in spring for climate/cultural reasons, it's even lower in real life, because over half of all people are born in less than 3 months. The pigeonhole principle remains unaffected, though.

[@muttcrewmusic]

The step from 75 to 366 reminded me of the old 90/10 rule of thumb for software development projects, i.e. the idea that you get 90 percent of the work done in 10 percent of the development time and the last 10 percent of the work take up the rest.

[@Vinkelslips]

4:02 GAH! That unfilled dot really gives me the creeps

[@dhtsoaedsdhtnadi9575]

in school, 30 kids in a room, NOT ONE OF US EVER HAD THE SAME BIRTHDAY.

[@MrPOKER725]

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

[@kerys_n_c]

What 😭

[@MrPOKER725]

​@@kerys_n_c Noot... Noooot...

[@misswilson_heather]

This is so interesting. I am a teacher and I have two students in my tutor group of 25 that share the same birthday and I still thought the number would be much higher when the question was first posed 😂

[@richardslater677]

What is the significance of “23 choose 2”. I know that there are 253 pairs from 23 singles but how does that contribute to the paradox, given that 366 choose 2 is nearly 67,000.

[@asdbanz316]

this is almost the same as comparing 253 total stranger's birthdays to yours. You also get ~50% of a chance (1-1/365)^253 I said almost, cause there's still a chance that none of 67000 people would share your birthday. But if you think about it, there's still a number of people which will give you 100% - population of earth minus all people who do share your bday plus 1

[@cigmorfil4101]

It contributes because when people hear the "paradox" they think that of the people in the the room in which they are with 22 other people, it must be one of the other 22 people who matches with _their_ birthday - only thinking that there are 22 possible matches and thus unlikely, whereas there are in fact 253 possible matches (as other people in the room could match with someone else in the room when they match with no one), increasing the likelihood of a match being found between at least two people (if A matches B and A matches C, then B must also match C giving 3 people who share the same birthday).

[@TheCurvalishis]

There are 24 board members at my job. JUST this week, I was making a list of all their birthdays and was surprised to see two of them shared one! I wondered what the odds were, and I guess now I know!

[@KM-uw4ez]

The kicker is in the wording. The odds of ANY two in the room having the same birthday, not one specific. Such as “how many people have to be in the room with YOU for it to be more likely that one of them and YOU have the same birthday “

[@c-9233]

All through my school days, in various schools, we had classes of around 30. There was always two people shared a birthday.

[@chinmayvaze]

Idk why but its just satisfying to watch you write

[@bexsta7766]

I thought that as well 😊

[@QuickHillFilms]

Loved your choices of music. I recognized each one and they all take me back to much happier times.

[@WrathofMath]

Absolutely, music is a magical thing!

[@papayongsarninei8133]

We did conduct a survey in my high school day on this theory .Out of 24 classes with about 40 students each , every class had at least one pair of students who had same birthday , some even had four pairs .

[@DIZIZNOTAMOON_LOOKCLOSELY]

Then i'm so bad in luck to not have even a single classmate with the same birthday as me? for 16 YEARS? 16 SETS OF CLASSES?

[@papayongsarninei8133]

@DIZIZNOTAMOON_LOOKCLOSELY It's about " same birthday " , not a particular date of birth .

[@willmichael138]

@@DIZIZNOTAMOON_LOOKCLOSELY None shared a birthday with you, but it’s more than likely there were pairs of your classmates who shared a Birthday with each other.

[@PeterBaumgart1a]

Great explanations of a classic. Question for you or anyone willing to give a good answer: Is there an "intuitive" way to understand why 253 (the number of pairs of people in a group of 23) is not simply equal half of 365, but quite a bit (~40%) larger?

[@genreynolds6685]

No. It’s just how perms and comb work.

[@EmerikFogl]

Jim Carrey approves

[@edgarlarios1829]

Topsy Kretts

[@Duncan1974]

This is a good explanation, I was thinking more along the lines of 1 in 12 for the month and 1 in 31 for the day...some sort of calculation based around those factors would get you a similar answer...?

[@peterbaruxis2511]

Me too except I hesitate to accept the above as a good explanation.

[@TheNonusVomica]

Not all days are equal. Births are often scheduled appointments with induced labor. That scheduling intentionally avoids certain holidays. People have “relations” more often in certain seasons, which weighs the scale. There are other factors, that when added in, influence the outcome even more. 23 as a raw number is a good start from a base mathematical standard, the real number is probably a touch less maybe as low as 20 or even 19. Simply because the distribution is significantly weighted to favor specific days.

[@genreynolds6685]

The author made it clear that he was assuming all days were equally likely, for illustration. Clustering of births on certain days makes matches even more likely, as you say, so it doesn’t weaken his illustration. The point is that many people think it almost impossible that there would be shared birthdays is a small high school class or college seminar group. That the breakpoint value (p > 0.5) is as small as 23 is the point. If the breakpoint is even smaller, which it probably is because of the clustering you mention, is beside the point. If some complication that he left out increased the required number, then it would be important to re-evaluate the assumption of randomness in birthdays.

[@twelvethirtyfour]

This is so dumb. He literally says let’s assume all days are equal.

[@scooterhocfecit3685]

I was reaching an engineering lab of about 25 students at USC back in the mid 1990's when I first heard of this. I tried it on the class and the first person I called on had my birthday.

[@jeffreysherman8224]

Other than the flagrant violation of calling a truth of mathematics that seems unlikely to most people a paradox, excellent video.

[@BenDRobinson]

I was horrified at such use of the term "paradox" so I stopped and looked it up, and it seems that's what the term "veridical paradox" means. What a paradoxical bit of nomenclature! So I guess we can now call any surprising piece of information a "veridical paradox" - that 91 is composite, that 7x11x13=1001, that Trump remains popular, ... such a paradoxical world we live in!

[@AlexEvans1]

So, horrified to realize that your understanding of the term paradox was wrong?

[@BenDRobinson]

@@AlexEvans1 'wrong' is a strong word for someone disagreeing about what can or can't be covered by a vague subjective term.

[@anaesthesiaregistrar8900]

Thanks I watched the same concept on vsause's channel but I couldn't understand it but now that I have seen this I get it

[@rainmannoodles]

Another "generic" way to explain why the probability is so much higher than we intuitively expect: If you have one person, and you add one more, you're only checking if the new person has a birthday that matches *one* date. But the third person can match *two* dates, and so on... each additional person adds to the pool of existing birthdays so by the time the 23rd person is checked, you have 1+2+3+...+22 = 253 checks, and thus 253 chances for a birthday to match. It's not an exact parallel since not all of the 253 comparisons are independent, though, so the 253 number isn't really valid except as an illustration.

[@joanbennettnyc]

I can guarantee almost 100% chance of matching birthdates to only TWO people ... if I limit my population to twins

[@Drogobo]

this actually happened multiple times in my elementary school

[@WrathofMath]

It did in mine as well because there were twins in my class haha. Eventually they left, and by senior year my graduating class was I think 27 people strong with 27 distinct birthdays.

[@davidjsanders76]

We had 3 in my grade of 155.

[@gen1kk]

man, what a great time I've spent now - thanks!

[@adamp2029]

Why is this considered a paradox? It’s just math.

[@WVMS42]

Because it is not realistic only in theory mathematically

[@adamp2029]

@@WVMS42if it’s true mathematically, it’s true realistically.

[@WVMS42]

@adamp2029 I doubt that, try empirical tests and you'll see

[@stevethomas3502]

Agreed, it’s not a paradox at all.

[@adamp2029]

@@WVMS42 ok, I will. I’ve found NHL team rosters online that include birthdays. There appear to be between 24 and 26 players per roster, with 32 teams in total. According to the math, there should be about 17 or 18 teams that include at least 2 players who share a birthday. I’ll go through the teams when I have the time and post the results here. Edit - I just looked over the first 3. Carolina Hurricanes - Brent Burns and Riley Stillman were both born on March 9. Columbus Blue Jackets - Jack Johnson and Ivan Provorov share January 13. New Jersey Devils - Shane Bowers and Jesper Brett share July 30. I’ll do more when I have some free time. And btw, I stop when I find the first match on each team. There may be more.

[@yuriridley8144]

Him: [speaking about people and dates] My mind: ❄️🐧⛄⭐

[@gbel78]

5:59 they do have one big leg tho

[@manchobbit]

I once worked in a team of 14 people - three of us had the same birthday. Not only that, our birth years were sequential!

[@idiotburns]

1:30 feels wrong already

[@Him4679]

True. 1/365 ≈ .003

[@asdbanz316]

@@Him4679 which is equal to 0.3%

[@williamwagner79]

Not to mention why did he include the year?

[@Caleb-Reid]

​@@asdbanz316I may be wrong, but wouldn't .003 come out to be .03% where 1.0=100%?

[@Fleja]

​@Caleb-Reid you're correct

[@markiefufu]

I worked in an office with around 60 people. The receptionist and I had the same birthday. We were in a string of birthdays. Someone in the office had a birthday everyday from June 28th to July 7th. We basically had cake, cupcakes and other party supplies for 2 weeks straight every year.

[@oh2sail]

Dd/mm/yy is a birthDATE not a birthDAY. For two random people to have the same birthDATE, it would be far more unlikely. You’d have to add in the probability of birth years being the same.

[@old_man_fran]

Don't want to be THAT guy, but... yes he wrote a date. Then the example question is about sharing the birthDAY. Birthday is included in the date. The question is not about the date

[@AdamAdam-vu3qt]

Nobody asked captain obvious.

[@cigmorfil4101]

For a school class where the ages are similar, there is a fairly good chance that the year will match also.

[@AdamAdam-vu3qt]

@ thanks captain obvious.

[@manushrieverma9029]

please connect the dots completely to the line when youre drawing

[@PeterVanHertum]

1:00 The probability for 1/365 is for dd/mm (anniversaries ?), but not for dd/mm/yy (birth dates ?)

[@leeroy8936]

I served with a guy that has the same birthday as me, we both joined the army on the same day, and both ended up in the same unit.

[@erikev]

This might be a paradox for simple minds. For most people this is pretty obvious.🤯

[@wayneyadams]

What you have for the pairings is a combination problem problem, i.e., how many combinations of 23 items taken 2 at a time. This was something i learned way back in twelfth grade (1965-66) when, in addition to A.P. Calculus, I also took a fun class called math analysis, that included logic, probability, and several other topics. The equation for that calculation is a simple equation using factorials. The symbol for factorial is !. For example, 4! = 4 x 3 x 2 x 1 Combinations of n items take r at a time. The n is a superscript, and the r is a subscript. nCr = n!/[(n-r)! x r! in this case, n = 23, r = 2. 23C2 = 23!/[(23-2)! x 2!] C = 23!/[21! x 2!] C = [23 x 22 x 21 x....]/[(21 x 20 x 19 x...) x 2 x 1] C = [23 x 22]/2 C = 253 There are 253 combinations of 23 items taken two at a time.

[@arunpokhrel5609]

I did a bit different approach but is equivalent to the combination of numbers and got my answer as 20, also 20C2=190, and 190/365 > 0.5, so answer should be 20 in my view.

[@cdprince768]

You made a major mistake at 0:43. You don't include the year in the birthday, otherwise the odds are far, far lower.

[@c.jishnu378]

Infinitely lower.

[@thephilosopher_original]

nail cutter needed badly

[@peterbaruxis2511]

At 7:10 you begin a process that would end with 1/365. The problem with that is that that last person actually has a 1/2 chance of having a unique birthday or a birthday that is the same as one of 364 other people (when none of the other people share a birthday, so therefore even a greater chance of having a unique birthday,) owing to the likelyhood of at least there being only two of 364 people sharing a birthday. Please stop "running the numbers" and equating mathematics with probabilities. I realize I'm focusing on the last person but as the likelyhood of a pair of previous people sharing a birthday inreases the denominator must decrease as the numerator decreases.

[@michelkuhne5787]

Nice treatment of this great classic, thank you! The idea of ​​considering pairs of individuals to make the conclusion more credible is interesting and original, well done! When I dealt with this problem with my students, I used a fairly effective reformulation: Imagine a 20 by 20 rack where you throw marbles at random. You can see that after around twenty marbles, you will have to start aiming to reach a free square, right? This convinced the most skeptical and prepared them well for the effort required by combinatorial justification. What do you think?

[@seephisd]

I'm stopping at 3:25. I can't see the paradox. I've got chess to play before bed. If it's solvable at the number 23...not a paradox.

[@musiclifegage7370]

I stopped at the exact same time. 😮 That's more of a paradox, in my opinion. 🙌🏼

[@mudai_]

Idk why I’m watching this, but I feel like one day it’s gonna come in clutch 😂

[@theclaybeartravels3596]

So are you saying that I need to buy 23x6 = "138" lottery tickets to get to the mostly likely chance that the 6 numbers on my lottery ticket will share the same numbers that are picked?

[@madmaddy102]

I have a question abt the probability. When you were doing the fractions for the chances of people not sharing a birthday, how (and why) do you know to multiply these fractions together. Sorry if it's a stupid question I haven't done stat in a long time

[@MrDifsh]

The probability that event A and event B both occur is equal to the probability of event A occurring multiplied by the probability of event B occurring.

[@zackmash851]

a simple rule you can follow is that if you're wondering the chance of one thing being true AND another thing being true, you multiply the odds. if you're wondering the change of one thing being true OR another being true, you add

[@ameerahmed6623]

1:09 1/365 is for same birthday month and day not year. one could be 1951 and the other 2010

[@ronevans4772]

You said exact same birthday, this means 2 folks were born on the same day of the same year.

[@BenDRobinson]

Thanks for introducing me to the expression "veridical paradox". I had to look it up, because for me the word "paradox" seemed entirely inappropriate here, as there is (to me) no apparent contradiction involved. So I now know that somethings that isn't really paradoxical at all, but merely slightly surprising at first glance, can be called a "veridical paradox".

[@WrathofMath]

Really appreciate this comment because all the people commenting "NOT A PARADOX" are irritating me intensely 😂 Everybody calls it the birthday paradox even though yes, it isn't a paradox, but yeah -the term veridical paradox really comes to the rescue here!

[@BenDRobinson]

@@WrathofMath for that matter a paradox is only a _seeming_ contradiction, so I suppose any given paradox will not seem paradoxical to someone who understands it well enough.

[@sgarstin]

​​​@@WrathofMathyou can't really blame them as the term "veridical" does not appear in the title lol But GREAT explanation of a truly counter-intuitive solution to a problem 👍

[@pkilpo]

That was good explanation. For me the probability calculus in uni was difficult so that I did not know how start calculation. For instance you solved this quite instantly using negative logic and then subtracting the result from 1. But how did you know it is best way at start? I would start with positive logic trying to calculate the probability directly. Why did you choose that strategy. I would like to learn that. Thanks for great video 😊

[@WVMS42]

Thank you very much for this interesting video, I'm glad it has been recommended to me 😊

[@steffernie]

I wish you were my math teacher in high school. I just know for some reason that I'd be excelling at something right now.

[@jimc9516]

and how did you arrive at those numbers??

[@TheReaverOfDarkness]

My manner of guesstimating the answer was to take the square root of 365 and add 1. I was a bit off at 20. I thought the way to calculate it would be to add 1+2+3+4... etc. until the total value reaches or exceeds half of 365 (182.5), and then take the highest number and add 1. This yields the result of 20, the same as what I got before. This seems right, because if you had 20 people, you would have 190 total pairs. There should thus be a greater than 50% chance that at least one pair share the same value, yes? But you said the answer is 23. What am I missing?

[@mibtedaislam44]

Jim Carrey: "They called me a madman."

[@ajinkyababar6072]

In my school class there used to be appx 70 students and every year at least 2 students shared birthdays on same date. I used to think it’s just a coincidence every year. Now I know the truth 😅

[@pugsnhogz]

I've seen this many times and it's always delightful to review. But I'm left with the same nagging question: how do I appreciate the curve of whatever we want to call the function that computes this probability? (n-1)(n)*(n-2)(n)... Like I want to make myself feel why, or be able to mentally approximate why, the answer for "365" is "23."

[@anonymousnoname3022]

Im imagining a room full of Spiderman pointing at each other.

[@DMCreator1123]

Can you tell me what is the probability of 2 people that work together share the same birthplace and same hospital and was born 3 days apart.

[@LeaNicoleK]

I met two of my best friends in a group chat of girls trying to make friends on tumblr. There were almost twenty girls in that chat, and the three of us stuck with eachother, almost nine years now. One of them and I share a birthday, month, day, and year. We live and were born in the same time zone. We were born 6 hours apart. I always think its so cool. I've met a handful of others with the same birthday but no one else that close.

[@bernardodconde]

came for the paradox, stayed for the mario 64 music

[@joshbahall6341]

I'm adding this comment at about 1:07 in the video but i noticed a discrepancy, for the year to be the same as well as the day and month the likely hood wouldn't be 1/365, 1/365 is for the day and month only you are assuming the people at random all are the same age, if u take a 60 year range the probability is 1/365 x 1/60

[@95rav]

Funnily enough, in a roomful of twins, you need a high number to reach 100% certainty too. Some twins are born just before midnight while the second just after.

[@thereturners7564]

In 1st grade, me and two others all had the same exact birthday - February 11, 1983 - and our teacher dubbed us the "birthday boys". That's the only time that's happened in my life, so far. I wonder what the odds become for 3 individuals?

[@nedim_guitar]

This was excellent! I checked out the choose formula and I get it now. I want more mathematics! Edit: Oh, I also subscribed.

[@WrathofMath]

Thank you!

[@genreynolds6685]

I would like to see the a priori derivation of how you got the 23 in the first place, rather than just retrospectively deriving the stated answer of 23. I see you could do it by brute force, multiplying the progressively smaller factors together in sequence (364/365)*(363/365) . . . until you got to 0.49, but is there a more elegant way to do it?

[@BenDRobinson]

Great question! My first thought was that you'd expect the answer to be somewhere near the square root of 365. I did some quick tests on the computer, substituting different values in place of 365. It seems the answer is always a bit above the square root, and tends to approximately 1.1774 times the square root as you go to very high numbers. I haven't yet worked out or guessed what that special ratio is! The question reminds me of something else I wondered about some years back, when wanting to communicate the size of factorials to people. I found myself guestimating that 100! ~= (40)^100. Seeing that I had implicitly felt that the nth root of n! tended to a specific ratio (which I'd estimated at 0.4) I wondered if that was really the case, and if so what that ratio could be. I thought 1/e might be a candidate. With a bit of testing I found that was in fact the case! Indeed, I ended up verifying (with testing and eventually with a proof of sorts) that n! ~= (n/e)^n * sqrt(2pi * n). To get back to your question, if you wanted to at least minimise the brute force involved, you could start your testing from 1.1774 * sqrt(n) (where n = 365 in the original question) and only test from there onwards. This would start you at 22 for n=365. UPDATE: I went to wikipedia, and found that the value ~1.17741 which I found emprically is actually given by sqrt(2 * ln(2)).

[@cigmorfil4101]

That is a perfectly acceptable mathematical method; it's called Numerical Analysis. Numerical Analysis is [usually] used when there is no easy way way to get a formulaic answer. eg to find the area under a curve which requires an impossible to do integral, the solution is to approximate the value numerically calculating the areas of small width rectangles and summing them - with the width appropriately selected the time of calculation and accuracy required can be achieved. One such method is the Runge-Kutta method used to find numerical solutions to differential equations. In this case, a simple numerical analysis solution is not only quick (a subtract, one multiply and one divide each loop), but accurate enough as the percentage increase with one person added is relatively large to cover rounding errors (until you get towards 45+ people when the differences start to be in decimal places, by 70+ it's into the second decimal place, by 80+ the third dp, by 89+ the 4th dp - it's reached 99.9991 % at 89 people).

[@BenDRobinson]

@@cigmorfil4101 but if an analogous question came up in a physics problem where you needed a good estimate of the answer when dealing with a number of particles in a significant mass - in the order of 10^24 say - instead of 365 - you would definitely want a more general formula. Luckily people have been keen enough to work one out!

[@mathewcheruvathoor4693]

Wouldn't figuring out the number of combinations of 2 with X give the answer ? So for X which would have 2CX greater than 183, a bit over half of 365, the value would be 20. I'd like to know how that is wrong, please.

[@Astrobrant2]

You showed one intuitive reason for why the number is as small as it is. Another reason is that the date that is shared hasn't been established. When most people think of this problem, they are probably considering the sharing of one particular date, when there are 365 choices of date that can be shared.

[@almightypancake2663]

i was thinking about my job during this, me and my friend share a birthday and we work at a summer camp. there are 26 camp counselors, so that was my guess. i’m pretty happy it wasn’t far off

[@biaberg3448]

We were about 20 persons from my family in a party some years ago. 2 of them were born on the exact same day, same year, but in different countrys. 3 of them shared the same birthday in September and 2 shared the same birthday in November. And later a child was born on her great-great grandfather’s birthday that also happened to be the constitution day in our country.

[@TheSoupLadle1984]

I grew up in a small town where our classrooms consisted of two groups of like 30 people, and that was all of us. And a lot of times people shared birthdays, so I guess it makes sense to me.

[@alfonsoalvarado8326]

You sound like Dr. Sheldon Cooper explaining something 😂

[@kimikanna_live]

if someone intrested, you need exactly 69 people in the room, to reach 99.9% chance that two of them are sharing a birthday So its even less than 75, which is quite impressive

[@cigmorfil4101]

To 1dp it is reached at 68 people (99.87% calculated to 9dp id 99.9% to 1 dp). At 99 people it reaches near certainty (you need to go to 5 dp to get 99.99995...)