Is the Birthday Paradox a Paradox?
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- Опубліковано 29 вер 2024
- Is the birthday paradox…Really…a paradox?
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Links and References:
betterexplained... (Regarding the birthday paradox)
www.bbc.com/new... (more on the birthday paradox)
en.wikipedia.o... (More on the birthday paradox)
dictionary.camb... (Paradox definition)
en.wikipedia.o... (Pigeonhole principle)
en.wikipedia.o... (Probability interpretations)
Credits:
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Now I feel bad for everyone born on 29th of february. Not only is it really hard for them to find another person born on their birthday, but they can NEVER get into that hotel!
Lol
its easy, just have your birthday on every year thats not a leap year set to the first of march.
Zupergurkan that is how you make it a paradox
i usually have my birthday on the last of feb, that way i can get i can get into a hotel 3 out of 4 years.. and for the record i have actually met a few people with the same birthday on the 29th
I always wonder when they choose to celebrate their birthdays on the years that are not Leap Years. Since February 29th is both the last day of February, as well as the day after the 28th, Which day do they Celebrate their birthdays when it isn't a Leap Year:
February 28th as it is the last day of February?
or March 1st as it is the day after Feb. 28th?
I love Statistics... I wish I retained more from class...
+krazed98 I suppose it is never late to learn what you want www.coursera.org/courses?languages=en&query=statistics
+Polla Fattah I was just thinking about how fascinating I find statistics, and how I wished I could study it.. Thanks!
thats technically calculus...
That moment I realized I don't watch this guy nearly enough.
This makes sense to me because i played a lot of poker. There are very few random hands that look 'random'. You just never see the cards come 2 5 8 J K with 4 different suits. There is always some kind of thing going on with the hand because there are so many possible things that can go on. If that makes sense.
The cards come out 2 7 7 7 K and that looks strange, or 4 hearts. That is what true randomness looks like. If the cards came out 'looking random' most of the time i would know something was wrong. The online players always complain about how the game is 'rigged' because of the strange combinations they see. But that is what i expect and i saw the same thing playing live poker.
I once had a class with three different pairs of people shared the same birthday who weren't related, AND a set of twins too who shared a birthday
1:06 - 50% of infinitly many rooms will have 2 people who share the same birthday
We had a guy from the States give a seminar about picking lottery numbers and probability of winning he likened to the birthday paradox. He said pick 30 random numbers - do not repeat numbers and place them into five lines. (six numbers per line for 6/49 lottery) He said if our class of about 24 or 25 would do this every week ( set of 30 random numbers placed into 5 lines for 5 tickets) for one year at least one of us would win a major prize. Could this be true? (Assuming 52 lotteries per year)
so we have 32 people in the same room and someone has the same birthday as me what are the chances then?
dude your all smart and stuff my mind is now a pike of mush laying on the bed next to me
That's pretty interesting Shakee. I've made a computer algorithm that makes 10 cycles with 100 rooms in each and see the results:
1 - 54%
2 - 56%
3 - 49%
4 - 47%
5 - 51%
6 - 58%
7 - 57%
8 - 58%
9 - 53%
10 - 53%
I just brought up the first 20 people in my family history database with known birthdays and what do you know 3 people in it had the same birthday.
Thank God for the subtitles.
I was thinking about this paradox as a kid, school...
Birthday Paradox: You tell people you want only one thing for your birthday, to get nothing. In this world, if you don't honor someone's birthday wish, someone else will. Is it possible to grant this person's birthday wish? Answer: No. If you get them nothing, then you are getting them what they wanted, which is not what they wanted(they wanted nothing, you gave them something). However, if you get them something, then you are not getting them what they want for their birthday, and someone else will try this impossible task and get just as confused as you are.
The amount of views for this video is a paradox also.
If there is a room with 365 random people, what are the chances that nobody will share the same birthday with anyone else.
0%
I am confused, I am pretty sure if i have 10 options and you then have the same 10 options the odds of us both getting the same are 1% not 10%. for instance if you roll a d10 and I roll a d10 the odds of us both getting 2 is 1%
not sure what is the paradox here
the probability that there will be at least a single shared birthday among 23 individuals in a 365 day year is 1 - 365! / (365 - 23)! / 365 ^ 23 ~= 50.73%
how many people would you need to has a 50% chance down to the second you where born. (ex. 7/5/1990 @ 3:42:53am)
Does it have to be the same year? If not then there are 4 ppl with 2 similar birth dates in my class so I can't really argue with this 50% probability
I have a classmate that has the same birthday to me and we came in the same school year
Didnt get the part after the beginning of thevHotel example
i didn't have the same birthday with sm at none of the school years that i had
why are there only 10 days of january, I probably sound stupid
Is it a paradox? Yes. The main definition of a paradox is: "A seemingly contradictory statement that may nonetheless be true".
It fits the bill perfectly. The 50% figure seems unlikely, but actually is true.
contradictory and unlikely are not the same
seemingly contradictory, and contradictory are not the same either
you should've explained what a paradox was first instead of assuming everyone knows what a paradox
kinda skipped to 6:55 where you are looking for someone else with the same birthday.
im born on the 9th of january, and i find it funny because i havent met a single person with the birthday 9th of january in my life.
I love math. Please fully explain this to us.
Wouldn't you have a 1 in 365 chance of having the same birthday as someone else?
but if theres like 70 people in a room, theres not 100% that 2 of them have the same birthday
In a class of 24 me and another girl in my class share the same birthday
why its wrong to do that?
chance of a person have the same birthday as you: 1/365
same chance with 2 individuals: 1/365 + 1/365
same chance with 3 individuals: 1/365 + 1/365 + 1/365
+Werex Zenok not how that works, with one person having the same as you it is, as you said, 1/365, chance for yourself and 2 others is not 3/365 as you can compare, yourself, with someone else, with that peron, compared to the other, and it goes on.
+Werex Zenok Use that logic in throwing a coin:
chance that after 1 throw you get heads: 1/2
chance that after 2 throws you get heads: 1/2 + 1/2 = 100%
chance that after 3 throws you get heads: 1/2 + 1/2 + 1/2 = 150%
If you're not sure in some probability calculation, just scale it down as much as you can, and you'll usually find out if there is an error.
Kopac Tunela Damian4447 Thank you guy. Now I understand.
Thats now how percentages work.
+DBZHGWgamer It does, 20 chocolates divided by half is 10.
with that, 2 halves ADDED = 20... (10+10(you know maths)). 1/2 +1/2 + 1/2 = 10+10+10
30...
If it were times it would be different... I'm guessing by now you already checked a calculator and figured that out, but ANYWAYS.... sup
what if someone's birthday is 29th of february?
he and vsauce are oddly similar, mostly bald
but if its you and you alone with comparations well...
it will never be 100% because well...reasons
But you made them have a birthday in the same month. What about the whole Gear?
oops... i meant year
24th of May, tomorow, anyone else?
in our class are 23 people and 2 do share the same birthday 😄
I was born on the 20th of April.
I don't understand how this is a paradox. Do you even know what a paradox is?
did anyone else think the A on the guys head was a party hat at first? lol
+Jolie Jackson Yep!
And I thought the B was a bra hat like from Weird Science.
Wait... It's not?
( ͡° ͜ʖ ͡°) lol no its supposed to be the A cause the next guy is wearing a B
nacoran lol
74th time watching and his accent is still the best ever.
I Think He is italian (like me) i also speak like this in english XD.
+MARCO D'ANDRIA In a video he said he was Arab
+MARCO D'ANDRIA nah clearly an arab xD
+LordDoucheBags A-rab
Arabic accent lol
I have no idea how i ended up at this video, but I'm kinda glad i did xD
same
+Luuk van de Pasch me too and the crazy thing is my birthday is the 9th January, and so is my mums
James Crawford Well there's this guy that went to the same children daycare or whatsitcalled as I and later on turned out to have an odd job as an instructor at the swimming pool I'm taking my lessons at and who's going to the sabe middle school as I, and guess what? We share the same birthday.
Lupinanx m.ua-cam.com/video/MRTOndSeNfA/v-deo.html&feature=share
I like the way he pronounces "r"
me too
I think He is italian (like me) so I Think Its The accent.
+MARCO D'ANDRIA Arab
+Bartosz Olszewski He's from Bahrain
I wish i naturally rolled R's like that... I don't think us Aussies can do it without it sounding forced. XD
Hope you guys like math...
+Sharkee I'm good at math , but i dislike math
I LOVE MATH...AND YOU!(no homo)
:D You are kinda like Vsauce :) a bit more math o.o ! Love your content !
+Sharkee I love Math when you do it.
+Sharkee I am not that interested in math and for me - personally - this was one of the less interesting videos on this channel. I will probably still watch it several times as I do with all of your videos to improve my understanding about what you're explaining.
Keep the good work up, Sharkee! This is one of my favorite YT channels!
What if you are looking for someone who has the same birthday as YOU, and you were born on February 29th?
+Nerissa Cappell then youre fucked or you can multiply by 4
+Nerissa Cappell about 1 in (366*4) chance but im too lazy to arrive to the actual figure
I meant what your chances would be based on different numbers of people.
A birthday on February 29th is equivalent to a birthday on March 1st during non leap years
+Joaking shouldn't that be 4*366 - 3 ?
There's an optical illusion at 1:12 between the boxes are dark circles :p
+Saturn Didn't notice, but now that I have, trippy AF.
whoa
What's the illusion i cant see it
There's these dark circles at each intersection if you pause at 1:12.
+Al El my brain is too smart to get the illusion so it doesn't get fooled but I showed it to a friend and he could see it.
Then the person whose birthday is Feb 29th walks into the room and says now do me.
+DarkBioCloud You leap year as well?? Commented then saw your post.. lol
+DarkBioCloud Thats what I was gonna say, there's a hole in the 6:00-7:00 paradox, Feb. 29th guy walks in, NO ROOM, SORRY
+DarkBioCloud Maybe there's a shed or cabin out back for leap year folks.
lol
luuuul, you're right
Bring twin into room
100% chance someone has the same birthday as you.
But twins don't necessarily share the same birthday.
umm yes they do, unless you're born like 11:59 and your twin is born on 12:01
Exactly, so the chance isn't 100 %.
Way to ruin the joke. :p
that's what I was thinking if there were twins there you go same birthdays
My brother is named "Guy A"!
+Ausussum000
GuyAUnderA
+Lithium Nonmetalide YEES
weird... my real name is Guy B, and I named my son Guy C... what are the odds? lol
GuyBUnderB and GuyCUnderC
Vsauce sure has changed.
+Lane Pitman IKR, It's awesome how his channel has grown since the vsauce shout out. (he's earning it though)
+Lane Pitman not really, he just moved to England and got this British accent...
and a tan.
What if I was born on February 29?
Woah
Duuuuuude
I was thinking about the same thing. It d make the possibility even lower.
45 people
That might lower the chances slightly
So close! I was born on Feb 30 and I just cannot find anyone else who shares the same birthday! There must be almost no chance someone in a group of 23 would share mine it seems :(
/s
This is my birthday paradox - I buy a cake and somebody ate it! Who did it!!!!
+Angry Face Me!
Da Foo Da Fook!!!
+Angry Face You did. You're buying your own cake so you're probably alone. Sad for you. :(
+Angry Face
The only paradox is that you bought your own cake on your birthday.
It is not a paradox that the cake was eaten - that is what cakes are usually for.
Zane enaZ It was an alone cake for me :)
Where P is the permutation function,
1. (365 days, 23 people, not pairwise distinct) 1-P(365,23)/365^23 = 0.507
2. (10 days, 3 people, not pairwise distinct) 1-P(10,3)/10^3 = 0.28
3. (12 days, 12 people, pairwise distinct) P(12,12)/12^12 = 0.0000537
4. (365 days, 365 people, pairwise distinct) P(365,365)/365^365 = 1.45 × 10^-157
5. (365 days, 23 people, WLOG equal to first one) 1-364^22/365^22 = 0.0585
6. (365 days, n people, WLOG 50% chance equal to first one) 1-364^(n-1)/365^(n-1) ~= 0.5, WolframAlpha tells me it's 253
7. (365 days, n people, WLOG 99.9% chance equal to first one) 1-364(n-1)/365^(n-1) ~= 0.999, WolframAlpha tells me it's 2518
8. (365 days, n people, WLOG 100% chance equal to first one) 1-364(n-1)/365^(n-1) ~= 1, WolframAlpha tells me no solutions exist
Time well wasted! :D
+Logo Well someone likes analytics ;P Btw, love how you stopped calculating it yourself at some point ;D
+Logo well...you know the function log_(364/365)(x) goes to infinity as x goes to 0...
there is actually a number that guarantees equal birthday to first. 7.349 billion ppl on earth atm, if was assume uniform distribution of birthdays (not including feb 29), then u just do [(population of earth)/365] + 1 and that number would to guarantee someone having the same birthday as you.
ofc there is a numbre if you assume uniform distribution of birthdays, but as he said in video if the birthdays are chosen at random there are no numbre of ppl that can guarantee some1 having the same birthday as you.
I got 50.7% as well, although I cheated and wrote a programme :P
did anyone else think the A on the guys head was a party hat at first? lol
+Jolie Jackson yeah :P
+Jolie Jackson Well its birthday paradox
i thought it was a party hat and B had a ribbon on its head until i saw your comment
I thought both things at the same time
The 'B' on the second guy is a bra. The birthday party got pretty wild.
I paused at the beginning and now I'll try to solve it.
First, let's assume nobody has their birthday on feb 29.
There are 365^23 of all possible arrangements.
There are 365*364*363*...*(365+1-23) unacceptable arrangements, which can be expressed as (365!)/(342!).
This is because the first person can have any birthday, the second one has one option less because it has to be different than the first one, the third one has two options less etc.
Subtract that from 365^23 to get the number of acceptable arrangements.
Finally, divide with 365^23 to get the probability of at least two people having the same birthday.
(365^23-(365!)/(342!))/(365^23) = 50.73%
That was the easy way. Now let's do the entire thing, with feb 29.
Let's take four years, which have 1461 days in total. There is one feb 29 and the rest are grouped by 4 of the same date.
Let's say each person chooses one of the 1461. This way we give feb 29 a lower chance.
Let's consider unacceptable arrangements.
The first person chooses one of 1461.
The second person chooses one of 1457, or, if the first person chose feb 29, one of 1460. The chance of the first choosing feb 29 is 1/1461.
The third person chooses one of 1453, or, if one of the earlier people chose feb 29, one of 1456. The chance of one of the earlier choosing feb 29 is 2/1461 (though I'm not certain about this part).
The n-th person chooses one of 1461-4(n-1)=1465-4n, or, if one of the earlier people chose feb 29, one of 1461+3-4(n-1)=1468-4n. The chance of one of the earlier choosing feb 29 is n/1461 (again, not sure here).
If there was 1 person in total, the chance of an unacceptable arrangement would obviously be 0%. (use common sense)
If there are 2 people in total, the chance of an unacceptable arrangement is:
1460/1461 if the first one was feb 29 (chance: 1/1461)
1457/1461 if the first one was not feb 29 (chance: 1-1/1461)
Together: (1/1461)*(1460/1461) + (1-1/1461)*(1457/1461), which is about 99.73%
If there are 3 people in total, the chance of an unacceptable arrangement is:
(1460/1461)*(1456/1461) if the first one was feb 29 (chance: 1/1461)
if the first one was not feb 29 (chance: 1-1/1461):{
(1456/1461) if the second one was feb 29 (chance: 1/1461)
(1453/1461) if the second one was not feb 29 (chance: 1-1/1461)
}
Together: (1/1461)*(1460/1461)*(1456/1461) + (1-1/1461) * ( (1/1461)*(1456/1461) + (1-1/1461)*(1453/1461) ), which is about 99.45%
If there are n people in total, the chance of an unacceptable arrangement is:
x*a1*a2*...*an + y*( x*a2*a3*...*an + y*( x*a3*a4*...*an + y*( ... y*( x*an + y*bn ) ... ) ) ), where:
x = 1/1461
y = 1-x
ai = (1468-4i)/1461
bi = (1465-4i)/1461
I wrote it as a c++ program:
const double x = 1.0/1461;
const double y = 1-x;
double a(int i) { return (1468.0-4*i)/1461; }
double b(int i) { return (1465.0-4*i)/1461; }
double birthdays(int i, int n) {
if(i==n)
return x*a(n) + y*b(n);
double out = x;
for(int j=i; j
Wow, all the asterisks got deleted because they represent bold text ...
You should imagine an asterisk wherever bold text begins or ends, I guess.
Gee Gee.
+RedsBoneStuff On mobile it's fine 👍
who else just skimmed past all of that?
Charter Hold tbh only the past before I started considering feb 29 is interesting. Which means the first 20 lines or so.
The maths for this is really simple (basic probability), and since the video didn't explain it, I'll make an attempt for those who are interested. The chance of at least two people sharing a birthday is the inverse of the chance that no one is. What that means is that if the chance of no one sharing a birthday is 25%, the chance of someone sharing one is 75%. The reason I bring this up, is that calculating the chance of no one sharing a birthday is really easy.
So, if you have two people in the room, the first person has his birthday on one of the 365 available days in the year. In order to not share a birthday with the first person, the second person then has 364 days to choose from. Add a third person, and assume as you must that the first two are on different days, the third person has 363 days to choose from. Anyway, all of these are pretty high odds on their own, but the thing is they all have to be true at the same time. To get the combined probability you have to multiply.
1 person: 365/365 -> 100% probability nobody is sharing a birthday
2 persons: (365/365) * (364/365) -> nearly 100% probability
3 persons: (365/365) * (364/365) * (363/365) -> still very high probability
As you continue to add people, the probability starts to drop more and more quickly, because each factor contributes.
TheSwiftFalcon
I did wonder, how the heck did he come with 50% ? I thought he just spit it out his ass. But by your calculation, (364/365) * (363/365 ) * (362/365) * (361/365) * (360/365) * (359/365) * (358/365) * (357/365) * (356/365) * (355/365) * (354/365) * (353/365) * (352/365) * (351/365) * (350/365) * (349/365) * (348/365) * (347/365) * (346/365) * (345/365) * (344/365) * (343/365) = 0.4927
That means, 49.2% chances of somebody not sharing the same birthday and 50.8% probability of somebody sharing the same birthday.
By the way, haven't finished the video yet at the time of posting the comment, I was just confused how to calculate this and didn't believe the 50% chance was real.
Thank you, this video contained too much simulating and too little actual math.
TheSwiftFalcon Thanks for clearing this up. Was totally lost at the end of the video but get it now after reading your comment :)
TheSwiftFalcon thanks, I was stuck. Looks like your explanation is also
1- (365 choose 23 / 365^23)
365 combination 23 being all unique birthdays. ~50.73% chance shared birthday.
Why do you use simulations to approach the probabilities instead of explaining the method that allows you to calculate them exactly ? It's not a complicated calculation at all, I'm sure many people would have been interested. Interesting video nonetheless !
Good idea for a follow-up vid!
+LeMageFro especially since they probably aren't actual simulations. Just pseudo-random combinations he made up
I agree. His explanation was so complicated because of the simulations that I couldn't follow it at all.
I'd like to know what the actual calculation is...
The trick is to realize that the event "this happens at least once" is the opposite event of "this never happens". In our case, if I write P(A) the probability of event A, we have P(two persons at least have the same birthday) = 1 - P(nobody have the same birthday). And the probability of nobody having the same birthday among N people is easy to calculate. I'm just going to neglect leap years here to simplify the problem a bit.
The probability of the second person not having the same birthday that the first one is 364/365.
The probability of the third person not having the same birthday that the first nor the second one is 363/365.
The probability of the fourth person not having the same birthday that the first, the second nor the third one is 362/365.
We see clearly that the probability of the Nth person not having the same birthday that the (N-1) other persons is (365-(N-1))/365.
Now the probability of having all these events happening at the same time (and therefore having nobody born the same day) is the product of all these individual probabilities :
P(Nobody born the same day among N people) = (364/365)(363/365)(362/365)*...*[(365-(N-1))/365]
=> P(Nobody born the same day among N people) = (364*363*362*...*(365-(N-1))/(365^(N-1))
where A^B is A to the power B
We can simplify this formula using the factorial notation [N! = N(N-1)(N-2)*...*2*1] :
P(Nobody born the same day among N people) = (364!)/[((365-(N-1))!)*365^(N-1)]
And finally we have :
P(at least two persons have the same birthday among N people) = 1 - [(364!)/[((365-(N-1))!)*365^(N-1)]]
We can verify that for N = 23, P = 0.507. That's the 50% chance mentioned in the video.
I hope this is clear enough, and sorry if having to write the formulas in line makes them confusing since it forces me to use a ton of brackets... If I made any mistake please tell me !
PS : if you try to use a calculator you'll probably have some problems with the last formula because 364! is too big of a number for most of them, so I recommend using excel to calculate
1-[(364*363*362*...*(365-(N-1))/(365^(N-1))] directly.
I was born 9 months after valentines day. I'm pretty sure that increases my chances of having someone with the same birthday in the room :P
ManiacBanana Years don't matter, only the days of the month
lol, i get it
Oh i get it
Lots of people I’ve met are born on November 14th lol
I thought guy A had a party hat on until guy B came in 😂
I thought guy b was wearing testicles on his face
I was looking at B wondering what the fuck kind of hat he was supposed to be wearing lol
2 videos in 2 weeks. Sharkee your doing it!!!! Vsauce status here you come!
+Kai Widman i thought vsauce status is a video a year
+Arab_Knight69 no that's CGP Grey status
There isn't 50% for me, I was born on a leap year.. :P
+Wizborg leap day?
Yep, 29th Feb.. I'm only 9.. lol
Wizborg My cousin too. He turned "five" this year.
Jeffrey Conner What's a leap second?
Jeffrey Conner I looked it up, but I don't understand your point about twins.
That awkward moment when UA-cam automatically turns on closed captioning but you can understand the dude just fine.
fucccck, I was wondering why my phone did that lmao... I didn't even think that it was because of his accent, I could understand him perfectly lol
very well put! you are getting better every video :) i wish you success and luck!
" What is the chaiiinncceeee, that twhou of them.. would share.. the same.. borrthdey "
Literally had me laughing at the start xD
*sigh* Why doesn't he at least show some of the math? In the ten-date example, there's a 90% chance that the first two guys don't share a birthday. If they don't, when you bring in the third guy there's only an 80% chance that he won't have the same birthday as either. So, 80% 0f 90% is 72%, and that's the chance that none of the three will have the same birthday, and 72% from 100% is 28%.
How he shows the rate of change between a factorial to another relation is cool as fuck for people who don't math as well as you (hotel vs just your birthday). It's more of a pedagogical exercise than anything.
***** I'm hardly Alan Turing, but I get your point. Still, he could at least have explained _why_ the figure is 28%, to ease people into the use of the actual math. As a means of teaching math it's poorly done.
But knowing how he came to that exact number wasn't really the point of the video. The point was to show the basic principles behind it with examples that are really easy to understand. Also, math can turn people away.
With the help of this video people will understand the basic principles and it makes it way easier to learn the math behind it if they are interested. This video was made accessible to as many people as possible (what I mean is that it doesn't really require any understanding of math). And I think it was a good decision.
I think there was an episode of _The Simpsons_ about that very concept of teaching math.
!
sorry i lost you after you said paradox
+stephen allen || @ 0:47? nice.
And if you would listen more closely you would hear that he said it was called a paradox, not that it is paradox. If you would watch until the end you would hear him say that it is not a paradox.
Bartek Strukowski ok, and this has something to do with my comment?
+mineo321 whoops why was I in my old account
If you think it doesn't have anything to do with your comment you're probably right. I guess I just missunderstood what you meant ;)
6:10 Well, you'll have to add up one more person to the already 366 "booked in" to make it to 100% since you have to take into account leap years.
There are 26 apples in a basket. If Mike takes 10 apples and Shannon takes 9 apples, what is the probability that anyone gives a fuck?
nice crashcourse on basic statistics
nCr and binomial expansion in exams. Kill me pls
Ez
Pretty easy stuff! Wait till you go to college! It gets worse there!
Easy* Clearly you're not studying language in college. ( Just kidding I couldn't resist :P )
ok
+Jeroen Bollen I have always been pretty good in maths on every topic we had, but when we learned about all those stuff ( don't know how it's called in english) I had the worst grades ever! I'd just say it is not for everybody and I'm glad that I don't have to know this with what I am doing right now
Why am I watching this? I hate math...
Maybe you have a secret love for math (AKA maths in the UK).
same
Sharkee video!!!
YES!!
Why did people start calling it a "Paradox"? Doesn't make alot of sense to me since Paradox means that something is negotiating itself ...
Having heard about it a few times before it is commonly referred to as the "birthday paradox", he finishes the video saying that it is not actually a paradox
Alfie Hansen you are telling me nothing new .... Its obvious that it is no paradox thats why I ask why it is reffered to as one...
I did say, it's just commonly referred to as the "birthday paradox", always has been
Alfie Hansen That its called like this isnt the reason it is called like this. You are turning in circle with no start like that
A paradox in general terms is when an idea starts logically (or illogically) but the conclusion derived from it is/seems illogical (or logical). To the general population, the conclusion of the birthday paradox seems illogical, so it makes sense to call it a paradox.
How many people would you have to fit in a room so there is a 50% chance that two people are born on the 29th of February?
+Bob Kerman That's a fun question
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+Aniruddh Sisodia not quite, the 29th of February only happens once every 4 years so as it happens 4 times less, the odds will be 4 times smaller, so the number of people needed will be 4 times larger than the number of people needed for there to be a 50% chance than someone shares your birthday
+Mk Jackary Then you are not choosing the birthdays from a uniform distribution. Even if we choose that all birthdays were uniformly distributed across the year, it would not be exactly 4 times smaller since the probability of beeing born on the for example the 18th of May is 1/366 buring a leap year while it is 1/365 during a normal year.
I share a birthday with my aunt, a woman in my school, two people in my church, and would've been the first one vaccinated in the movie Contagen.
My sister was born on the same day as me... four years after.
+Jack Evans That probably has more to do with your parent's sex life than anything. My girlfriend and her two siblings are all born in late august/early september because they were conceived in the winter months, when its cold and nobody likes to go outside.
My little brother was born on my birthday 15 years later
+Martin Chabre shut up lol
I was born almost 9 months to the day after my parents ' anniversary. Go figure.
+Nathan Drassinower A noticeably large percentage of the european population are born 9-ish months after the football world cup ends. so, thats a thing.
here is a related problem:
let's say you have an infinite hotel like you discribed but with full occupancy.
suddenly everybody is assigned a random room number and moves to their new room .
now these numbers were assigned at random so multiple people can be assigned the same room and there can be empty rooms.
What is the chance a room will be left empty? The math tells me 1/e but if there is an infinite number of people that can be assigned a room number than why aren;t there an infinite number assigned?
Also why is the chance of having only one person assigned to the number also about 1/e
+Jakob Virgil What !!!
Yep, no uniform distributions on infinite sets.
Although there are interesting properties in large but finite hotels.
+choralbird the problem is valid if you use limits. Basically the wording becomes "As a hotel gets arbitrarily large, what happens when etc etc"
at the limit, then the probability of selecting any room tends to zero. Thus it conforms precisely to the notion of "almost never". Infinite tenants aren't a problem, but infinite rooms _are_.
at the limit only 1/e rooms are empty
When you read the subtitles when he said no...
6:56 Hey! My Birthday is really in 9th of January!
Mine aswell. :P
GET IN THE ROOM
JthayerTheGamer NOOO
Mine too. D: impossible, what sorcery is this?
1780 viewers can say the same thing ^^ (650k/365, or 1/365 * 650k)
Finally! Some who has the day/month order correct instead of slavishly following the illogical American order of month/day
OMG YAS
I'm an American and I wholeheartedly agree.
Why is it illogical? I agree that day/month/year makes more sense, but that doesn't make month/day illogical.
Why is it illogical? I agree that day/month/year makes more sense, but that doesn't make month/day illogical.
Why is it illogical? I agree that day/month/year makes more sense, but that doesn't make month/day illogical.
paradox
noun /ˈparədɒks/
seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true
I came here looking for someone to point this out. The birthday paradox exactly fits that definition.
Elwood Hopkins It's really starting to annoy me. "Paradox" is the new "centrifugal force" of the internet. Nobody can use the word anymore without someone going "uhm, actually ..." and be totally wrong about it. Do we need another xkcd first before we can lay this to rest?
thanks for understanding me +Penny Lane ; )
I thought a paradox was like a circle? Like there is no beginning or end because without one part the other wouldn't exist?
TheDoctorsDemon Perhaps you're thinking of circular reasoning?
God Damn i love this Indian tom scott
Actually, that was a pretty good paradox near the end. What are the chances of someone having the same birthday as you if you keep fitting people into a room? By the time you reach the population of the Earth, 100%. and yet, mathematically, it isn't 100%. The reason is, you know there are other people with your birthday, you have met some of them, so you know some of those people will get into the room eventually.
Thus, a paradox between what you know, and what the formula can work out, until you plug in the birth dates of every person within the case.
That's exactly what I was thinking :D
That's not really a paradox, it's just the difference between the theoretical and the actual.
it's not even that, it's just that reality doesn't have an infinite pool. if you did the theoretical again pulling random people from a set pool of everyone on earths actual birthdays, then it's 100% and no paradox.
Exactly - in an "infinite pool", each person would have an equal chance of any given birthday. Since there are a finite number of people on the earth, then every time you put one person into the room, that is one less person with that birthday in your pool to pull from, so the odds shift every so slightly.
Actually, if you'd bothered to look up the definition of "paradox" you'd have seen that, actually, yes, it is in fact a paradox, simple as that.
An important remark about this paradoxe is that the probability is calculated under the assumption than all the birth dates are equiprobables, but statistically this is not exactly true (holidays for exemple have an important influence of the dates of birth). Therefore, the actual probability of having at least two similar birthdays in a group of 23 people is higher than 50% .
I always loved this problem and even had it in a job interview! The common trip-up I find, and he touched on it, is an individual will think, "there are 23 other people in the room, the chances that I have a birthday in common with any of them can't be that high." and right you are, but that is not this problem! Realize that each and every other person in the room is also making comparisons not always involving you. That's a lot of comparisons and it only takes one hit to be counted!
Anyway if you care about the math, read on, it is simple but not necessary to grasp why the chances get high fast. You want the [number of hits] divided by the [total possibilities]; that will give you the [success probability]. Turns out it is easier to do the [number of fails] divided by the [total possibilities] and then just do [success probability] = 100% - [number of fails]/[total possibilities]. There are 365 day-slots so "n people" can each be in any of those so there are [total possibilities] = 365^n/n!. Notice the n! is the bottom is because we don't distinguish individuals (Matt and Ann in Jan 1st slot looks the same as Bob and Sarah in the Jan 1st slot). In order to fail, nobody can be in the same day-slot, so just fill them in one by one. The first person has 365 day-slots, the second 364, the third 363, and so forth. Because we don't care about the order again (it doesn't matter if Matt is in the Jan 1st slot and Ann is in the Jan 2nd or vice versa), it is a combination or [number of fails] = C(365, n). Putting what we found together: [success probability] = 100% - n!*C(365,n)/365^n. Put in n = 23 and you will find that ~50%.
+LlosaTheKing It was for a janitor position at M.I.T.
+Jeff Johnson There was a software tech place a year or 2 ago that was asking it's applicants "why manhole covers are round?" I forgot where I heard/read about it though, or even what the tech place produced (I think it was software oriented though)
it wasn't directly applicable except that it was quantitative in nature.
Wow, that was the best explanation I've ever heard on this problem. I have never seen the reasoning so clearly, thank you!
What if my birthday is February 29th? :P
Your birthday will be counted as 28th of february
Peliministeri
But that's not my bday :(
Well, think of it this way. Dates are numbers made up by humans to structure part of society. Nobody really has a birth day.
Actually It would be more logical to count it as March 1st on non-leap years.
+Jim Your logic is arbitrary. I'm sure you consider it more logical because both come directly after February 28th, but that is as consistent as saying that February 28th and 29th both come before March 1st, and we should group them together in that way. You don't sound smart when you use the word logic, kid. All things are arbitrary.
What about February 29???
ikr
i was gonna say that! >:(
What about sharing the same year? Same month? Same month year and day? Same headshape? Same shoe size? Same waist-to-hip ratio? Same gender? Same interests? Same member length???
Identical twins.
I now want to name my child guy A
Once in one of my middle school classes our teacher split the class into groups of 5 for an assignment. We were suppose to find out whoever was the oldest to determine a "leader." However, another kid and I were born on the same day and tied for the position.
Should have used time of day you were born to resolve it.
Aaaand, in a test group like that you have an additional factor - you were all (probably) born within the same 12 month period. But in your example, how many groups didn't have a tie?
I keep thinking he's going to tell me my computer has a virus and he can fix it if I give him money.
shocking! just last night i thought of catweazel and looked it up!
Chris R That's spooky.
So why wouldnt this be true at my school? Where we have ~300 kids and not many share birthdays?
+TheGreatWazoo Is there at least two people who share their birthdays? There doesn't need to be "many" to verify the preposition, only one couple.
When you flip a coin, there's 50% chance it'll land heads, but it is possible to make 10 flips and all land tails, but it is very unlikely to happen (the chances of that happening is 1/1024).
The chances of two people sharing their birthdays in a room with 23 people is 50%, but the chances of it happening again in the same room is 1/4 (or even less if you disregard the first two on the second run), and the chances of a third person sharing the same birthday as the first two is around 6%.
Try dividing them at random in groups of 23 and seeing for yourself
thats true, the peoplewith the same birthday may have ended up clumped
Just because you don't know the people who share birthdays, doesn't mean there aren't a lot of them.
Also, it can be a bit hard to tell when birthdays coincide in large groups. I ran a little program that produced 23 random numbers between 1 and 365 to see if the math holds up under experiment (it does, obviously), and it was quite difficult to identify which sequences had repeating numbers by eye (I eventually gave up and had the computer do it for me). I'm sure if you painstakingly took everyone's birthday and logged it in a spreadsheet you'd find many, many people who share their birthdays.
Hey.....know how many birthdays do you have???.....................Just ONE, of course. All the rest are anniversaries!
No.
"The Latin root word ann and its variant enn both mean “year.” These roots are the word origin of various English vocabulary words, including anniversary and centennial"
Hummmm...:"birthday. late 14c., from Old English byrddæg, "anniversary celebration of someone's birth" (at first usually a king or saint); see birth (n.) + day. Meaning "day on which one is born" is from 1570s. Birthnight is attested from 1620s....................................or..........Merriam‑Webster--Define birthday: the day when someone was born or the anniversary of that day..........Your turn!!
+Bugdriver49 The word anniversary, as I already showed you comes from the Latin word for year. It pretty much means yearly celebration, or the sane date as something that has happened.
Okay.......It is becoming clear I'm once again in the presence of an alien. An Oblivian from the planet Oblivious. Oblivians are a rather moronic lot, not being able to discern the obvious even when they themselves are putting forth data refuting their own assertions. I allow you, Mr. Oblivian to ascend the stage and speak.....ahem: " It pretty much means yearly celebration, or the sane (sic) date as something that has happened.".............. Now, please correct me here. Does "yearly celebration" have the slightest correlation to "anniversary?" Now, Mr. Oblivian, PLEASE tell me how many BIRTH-DAYS one has??? In other words....how many times does one pass through the vagina of one's mother???? When "birthday" is used at any other time besides the day you were born, it denotes an anniversary. There is ONLY ONE DAY on which you are born!!..............Okay, okay I wouldn't really expect an Oblivian to understand word play or irony......But for the sake of Oblivians everywhere, please refrain from lowering the already low expectations we humans have of your ilk.
You have a birthday every year (noun meaning cellebration of birth). However you have only one birth day.(actual day of vaginal expulsion.)
the birthday paradox is a paradox because it says its a paradox in the name of the birthday paradox
WHAT THE FUCK??? 7:04 that's my birthday too!!
What are the chances that i'd see my birthday "9th of January" in a UA-cam video about birthdays?
Same here bro xD
OK - So anybody else born on *24 November* 🎂 ??
+WMTeWu 25th. So close...
+WMTeWu Me
+WMTeWu 23...
+WMTeWu So this means, out of every 4 replies to a youtube comment, 1 of them share the same birthday.
yup...
I got here from watching Minecraft videos. My poor brain :'(
+I comment on videos You need it. now stop watching minecraft and hit the books! >:(
+I comment on videos I got here from watching a clip from Doctor Who where the Doctor explains a bootstrap Paradox. So I can see the connection for me. Can't see how Mine Craft relates.
+I comment on videos
Minecraft?
WEEEEEEEEEEEEEB
lol jk
I don't even remember how I got here.. Seriously. What the freak was I watching that led me to this!?
davidinark Look at your UA-cam history.
omg this was slow. is this video made for 3 y olds?
It's made for a general UA-cam audience, so yes. Keep in mind though, that people consider this a paradox. People are really dumb.
This video is pretty information dense. Could you explain the topic in fewer words, with appropriate examples?
I think you're both confused because he talks fairly slowly. The information itself is well put together and he has very few superfluous points
No one's dumb, unless they have a mental illness and it's not their fault. Just ignorant. Not that it's a bad thing, either, to be ignorant. It's like calling a 9 year old from North Korea an idiot because they don't know North Korea isn't the best of all time. A lot of schools suck so a lot of people won't understand math that goes a little deeper than the obvious adding and multiplication.
+Darian P It's not really that information dense. He lingers too long on every point besides just speaking slowly. He's laying down a road that an infant can walk down.
+Shane Benjamson Your thoughts are a little scattered. You're trying to say more than you can. Stick to a central point.
Besides that, I'll try to talk about what I think was your central point. It is clear to me that there are more people besides just the normal and the mentally ill on the spectrum of intelligence. Actually, I think that there are two main categories of intelligence, namely, comprehension and self-sufficiency. Comprehension being how easily you understand something, and self-sufficiency being how much you can accomplish mentally by yourself without help. Both types work together to produce how well we can think. What we were talking about is that this video has a very low comprehension level, so that many people can understand it, but also caused us to become disinterested. We didn't bring up knowledge or ignorance, so I won't mention that.
But populations dont mate on random days, a lot of time mating trends on or around holidays, so in real life, this situation is improbable, but good video anyways.
It's actually even more likely to occur if you assume people are more likely to be born on some days then others. Take it to the extreme and assume that people can only get pregnant in the month of January. That would mean that everyone's birthday would be around October effectively limiting the number of birthdays and increasing the likelihood that any two people share a birthday. The 50% at 23 number comes from assuming a perfectly even distribution. If the distribution is skewed in some way that likely hood goes up not down.