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: ua-cam.com/play/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO.html Join Wrath of Math to get early&exclusive videos, lecture notes, music, and more! ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
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.
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.
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.
@@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"?
@@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.
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.
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
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?
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
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.
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.
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 .
Reminds me of the silly puzzle question : "If you have 10 black socks and 10 red socks and you can't see the socks then how many socks would you need to pull out of the pile in order to definitely get a pair.
I have met a person born the same day, the same month and the same year as myself, albeit in a different country. Oddly enough I noticed that we had fairly similar characters.
I was almost there before the explanation. I went for the smallet number when factorialed that would give a number greater than 365/2. Which is 6! However, it's not 6x5x4x3x2 that I should have been calculating. It's 6+5+4+3+2+1. Therefore, its the smallest number when all of i and all of its smaller integer numbers are summed have to be greater than 365/2, which I guess is 23.
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.
The heuristic or practical method:Throw 75 elements randomly in a 19X19 quadrats-net(O.K. Its 4 or about 1% less than 365) and with about even more than 99.9% probablity 2 fall in the same quadrat.
The problem with this video is that it is just blanket math. The problem with that is there are some very common birthday days. Some days with almost no birthdays and some days in a range where many many birthdays happen. So the real number is smaller than 23.
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.
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.
@@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.
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.
Why are we multiplying to calculate the probability? I think the answer should be 20, not 23: If you have two persons, the chance they match is 1/365, with three persons 1/365 + 2/365, etc. If you add those, after 20 persons you have (1+2+3+..+19)/365 = 52% cumulative chance that the 20th person added to the group makes a match But I probably don't know anything about probability! 😅
We did this experiment at school multiple times and in multiple classes, and every time there were always two of the class with the same birthday... But that's what happens when I have a twin brother😂
If you could somehow account for parents' "liking for activities" on major holidays and the nineish-month offset, statistics would probably be skewed slightly and would most likely be displayed via graph instead
It's funny you mentioned this, a number of years ago I belonged to an organization and it was striking to discover how many of us had a mid-November birthday.
I've had this explained mathematically so many times and for a second it makes sense. But I still cannot visualize this and it seems like a trick of the numbers. Can anyone point me in a direction of a complete visual breakdown of this?
*@ Wrath of Math* -- You could do the calculations for us for the number of people in the room where three people and four people share a birthday, and that it is likely.
I've seen dozens of videos and explanations about this problem, and I'm still waiting to see who will be the first to physically go out on the street and ask 23 (or 75) different people what their date of birth is, and show us in reality what the math says. I'm still waiting for this video... Will you consider to be the one who actually prove it, and makie such a video? I think you will have 1M viewers.
I did it. Programmed randomly choosen 23 numbers out of 365 like 10000 times or more (10000 groups of 23 numbers) and calculated how many times there were atleast 2 equal numbers,and then just divided by 10000 and numbers are almost the same as exact probability.
I once met a person born the same day, the same month and the same year as myself, albeit in a different country. Oddly enough I noticed that we had fairly similar characters (although I am a man and she was a woman).
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.
Best indicator(s) of this are location between the "poles", cultural, religious belief systems, and species. Many people near the equator don't have children in winter months... but conceive them during that time period or late fall. (Exception is Valentine's Day) There are different variables connected to "why". Need/desire for survivability being important. Availability of food, the right conditions, etc...
My brother and cousin had the same b-day... not the same year. Both younger brothers and from a big extended family of religious devoted people. Ovulation cycles are another less discussed variable. "9 months of she is not available" is another indicator... families need women😅 and men know this.😊
My immediate family is an outlier, we have two sets of people born on the same day. My dad and my oldest son are both born on the same day and my youngest daughter and I are also born on the same day. I agree about the results, but there are still only at most 23 dates out of 365 which is why it seems weird on first look. If you consider it like you had 365 rooms and each had every person born on that day in it. You would not think if you randomly picked 23 people you would be more likely than not to grab two people from one room instead of 23 separate rooms.
Agree totally with the chances as calculated. However shouldn't we also be able to calculate by evaluating the number of "pairs" in the room. If you have 3 people in the room then there are 3 pairs so the chances are 3/365. If there are 4 people in the room there are 6 pairs, so the chances are 6/365.... We would continue until the number of pairs is 183. Why is this giving a different answer, what did I miss.
I think some teacher taught us the "number of pairs" version. I realized by myself that it is quite wrong. The results are close, but it is wrong. One malfunction of "pairs" is that even with 500 students, it still predicts a finite possibility that there are no birthdays in common! The correct calculation is way more complex, but it is perfect because as soon as you reach 366 students, the probability of no birthdays in common drops to exactly zero.
If we calculate those having birthdays in February for example we will have a higher probability because fertilisation happens often in spring (May for example) leading to a birth 9 months later 😊 However my bd is in May, I wonder what did my parents had in mind ?! 😳 😅😂
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".
Most people incorrectly think about how many people it takes for 2 of them to be more likely (> 50%) to have A specific birthday, eg Dec 27. That's not the question.
@@russellstyles5381ok, thanks for the clarification! So, with this, imagine if the 1st person has the bday on dec 27. So, according to the 2 differences of the question, what would be the probability of having the same bday by case 1) a specific bday and case 2) any bday for 3 persons to have a pair? Asking, Just to have a better clarification, if you don't mind! Thanks!
Shouldn't the first calculation be 1/(365*365) because person a and person b are both randomly picked? If one was known at the beginning and the other was random 1/365 would make sense. He switched from talking about 2 randomly selected people to 1 person with a specific birthday and 1 random person with a random birthday while discussing the math.
1/365^2 would be if these two people were to have birthdays on a specific given day. But since they are just supposed to have them on the same day, then the first person sets the date, and the second has a 1/365 chance that it will be the same date. Of course, leaving aside behavioral issues, such as people being more amorous in the spring, etc.
What he's doing is calculating the probability that no pair of people share a birthday. We don't know anyone's birthday in advance. We take the people in a random order and consider what each person's birthday can be so that it's different from everyone we have already considered. For the first person, nobody has been considered yet, so they can have any of the 365 birthdays available. This is a 365/365 chance. Since that is equal to 1 and multiplying by 1 doesn't change the probability, the person in the video glossed over that detail. The second person can then have any birthday besides the first person, leaving them with 364 options out of 365, and so on...
Uhm, if 2 share the same bd, your number goes to infinity. As, it's possible, you have a room of 366 people - all with the same bday. It's just as likely - right?
I can only say two things… 1. Given the fact a woman gives birth to a child somewhere in the world every 8 minutes the chances of meeting someone with your birthday in your lifetime is high…but low if you just randomly put 4 people in a room. The second thing is…I think you just like yo hear your own voice and the smell of sharpies!
This may seem unintuitive, but it 100% absolutely is NOT A PARADOX. PLEASE STOP CALLING IT THAT. Words matter. Definitions matter. There are many mathematical idiosyncrasies that are interesting and seem unlikely... but a statement that seems unlikely is not the same thing as a statement that contradicts itself, i.e., a paradox.
There is no one answer to that question as it depends on context. At the most literal, we may say a paradox is any statement like: P and not P. That is - something paradoxical/contradictory. In this context we're discussing what's sometimes called a 'veridical paradox', which means there isn't actually any contradiction logically, the only 'contradiction' is that the truth of the matter runs counter to our intuition, so it feels paradoxical. Often a 'paradox' is an impossible result that comes from seemingly reasonable premises, thus showing us there must be an error in our premises.
Hi . At 366 you still don't have 100% probability because of the leap years. Sorry for being a PIA but being a non-mathematician it still poked my eye.
@@russellstyles5381 Rounding before comparisons is a disingenuous practice. For example, if you round the probability to the nearest integer, you could say it reaches 100% at 23 people. Rounding should only be used for displaying values concisely.
This question obviously doesn't take into account that people are born more often on certain days. Example, mid October is common because they were conceived on Valentine's Day, December 25th is very uncommon because Christian mothers will deliberately avoid that day and will have the doctors induce an early pregnancy, which bloats the chances of the proceeding days.
This is true, but it's not super relevant to the problem at hand because that only makes it more likely that a small group of people would have a common birthday. So the 23 number is a worst case scenario so to speak. Assuming uniform distributions of birthdays, it takes 23 people. Accounting for the non uniformity would only increase the odds for 23 people sharing a birthday, and accounting for leap years is an insignificant change that doesn't add anything to the interest of the problem.
A twist: I belong to a Discord group of 20 people. A few months ago, we discovered that I share a birthday with two of the others. I think it's about 0.86% likely for 3 people in 20 to share a birthday. This number was greater than I expected; it's almost 1%. And for it to be more than 50%, I think it takes 75 people. I used C(group size, 3) ÷ 365² Did I do it correctly?
It's not really a paradox. And you didn't really explain it very well with the lollipop people, you didn't really explain how and why 364/365 running to 343/365 of not having the same birthday translates into 0.49. It doesn't feel intuitive to me with your negative explanation. I feel you skipped the intuitive part of that explanation. The dots however was more intuitive for me. If I imagine a room divided into 365 squares, and I ask 23 people to throw coins into the room, then to say it's more likely than not that there will be a square with two coins in it sounds quite reasonable.
Why can't we just do a more straight forward calculation? As you told in the beginning, the probabilities of persons sharing the bdays are: 1st person 0 2nd person 1/365 3rd person 2/365 . . . 183rd person 182/365 = 0.498 And for the 184th person 183/365 = 0.501 So, why not the min persons reqd to share the bday is 184?? - Which is just above half of the total number of days! It makes sense that way.. Ain't it?? Then, where's the issue or wrong in this?? Also, yourself mentioned that with 366 people, we can certainly say that 100% chance of finding a pair, and going by the same logic, with just more than the half of 365, should be >50%. Right?? But with 23 people, the 23rd person has a mere 22/365 app= 0.06% chance only!! 🤔 How's it correct?? So, the answer should be 184, not 23. Isn't it?? Thanks!
Each person beyond the second has a greater chance than the last to share a birthday with one of the previous people because the pool of possible birthdays that could be picked and be different is shrinking. You made the assumption that 183 people have different birthdays and the 184th person and anyone beyond that could have any birthday.
@@gamer122333444455555 Yes, in my approach too every subsequent person's addition increases the chance of getting a pair, without doubt - that's why you are witnessing the increase in the chance probability! No assumption is made whatsoever.. The chances of getting a successful pair is what is being obtained, with every additional person! This actually means, the chances of an existing bday sharing is actually increasing - which is perfectly valid and without any assumption! To emphasize more on this, even the 2nd person can happen to share the bday with the 1st person - but only the chances of such occurance is minimal - there's no form of assumptions, whatsoever! To explain in very simple terms, Minimal chance is for the 2nd person. (Just > to 0). Maximal chance is for the 366th person. (just > to 100). So, obviously 50% should be around the middle! (just > to 50). Simple!
@@gamer122333444455555No assumptions were made, whatsoever! As you rightly mentioned, each subsequent person has a higher probability of matching, than his previous one - that's absolutely right and hence 2/365 is greater than 1/365 and 3/365 is greater than its previous value of 2/365 and so on.. Reg the assumptions you mentioned, 183 people weren't assumed to be distinct - but only the probability of them to have matching b'days were identified. To be honest even the 2nd person can have the same b'day as the 1st person - nothing stops it, but only the probability is very less i.e. 1/365!
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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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.
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.
very silly oversight! Thankfully we didn't spend too much time with the mm/dd/yy, so hopefully it won't cause confusion
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.
@@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"?
@@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.
@@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.
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.
Using maths or facts to show that superstitious stuff is nonsense appears to upset people.
I have no idea why.
@@mattsadventureswithart5764 It's bad luck, that why! :D
@@IvanToshkov @mattsadventureswithart5764 You'll both get an invitation to the next party I throw.
Reminds of the Mitchell and Webb sketch about the brain surgeon and the rocket scientist.
Underrated space use 😂💯
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
Hahaha.
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?
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
Yeah, I only put the correction because in the video I was specifically discussing factors less than 1. A minor slip of the tongue!
I love when mathematicians can explain their concepts with simple logic
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.
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.
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 .
Reminds me of the silly puzzle question :
"If you have 10 black socks and 10 red socks and you can't see the socks then how many socks would you need to pull out of the pile in order to definitely get a pair.
Nice Mario 64 penguin world music.
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.
Feb 30?
Feb 29
I have met a person born the same day, the same month and the same year as myself, albeit in a different country. Oddly enough I noticed that we had fairly similar characters.
@@Potemkin2000what kind of calendar are you using?
This is sarcasm, I assume? We don’t ask everyone we meet, “What’s your birthday?” 😆
I was almost there before the explanation.
I went for the smallet number when factorialed that would give a number greater than 365/2. Which is 6!
However, it's not 6x5x4x3x2 that I should have been calculating. It's 6+5+4+3+2+1.
Therefore, its the smallest number when all of i and all of its smaller integer numbers are summed have to be greater than 365/2, which I guess is 23.
Thank you very much for this interesting video, I'm glad it has been recommended to me 😊
Great job, best explanation I've seen to date
Thank you!
this actually happened multiple times in my elementary school
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.
We had 3 in my grade of 155.
The heuristic or practical method:Throw 75 elements randomly in a 19X19 quadrats-net(O.K. Its 4 or about 1% less than 365) and with about even more than 99.9% probablity 2 fall in the same quadrat.
I love heuristics and really interested to it, do you have a good book to recommend?
The problem with this video is that it is just blanket math. The problem with that is there are some very common birthday days. Some days with almost no birthdays and some days in a range where many many birthdays happen. So the real number is smaller than 23.
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.
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.
Why is this considered a paradox? It’s just math.
Because it is not realistic only in theory mathematically
@@WVMS42if it’s true mathematically, it’s true realistically.
@adamp2029 I doubt that, try empirical tests and you'll see
Agreed, it’s not a paradox at all.
@@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.
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.
I love heuristics and really interested to it, do you have a good book to recommend?
Thanks. Great math story problem.
Great explanation
Why are we multiplying to calculate the probability?
I think the answer should be 20, not 23:
If you have two persons, the chance they match is 1/365, with three persons 1/365 + 2/365, etc.
If you add those, after 20 persons you have (1+2+3+..+19)/365 = 52% cumulative chance that the 20th person added to the group makes a match
But I probably don't know anything about probability! 😅
We did this experiment at school multiple times and in multiple classes, and every time there were always two of the class with the same birthday...
But that's what happens when I have a twin brother😂
If you could somehow account for parents' "liking for activities" on major holidays and the nineish-month offset, statistics would probably be skewed slightly and would most likely be displayed via graph instead
It's funny you mentioned this, a number of years ago I belonged to an organization and it was striking to discover how many of us had a mid-November birthday.
Enjoyed this even though I'm not a mathematician. What is the probability that a husband and wife share the same birthday? My parents did!
I've had this explained mathematically so many times and for a second it makes sense. But I still cannot visualize this and it seems like a trick of the numbers. Can anyone point me in a direction of a complete visual breakdown of this?
I have 53 years and I never knew someone to have same birthday as mine.
*@ Wrath of Math* -- You could do the calculations for us for the number of people in the room where three people and four people share a birthday, and that it is likely.
I've seen dozens of videos and explanations about this problem, and I'm still waiting to see who will be the first to physically go out on the street and ask 23 (or 75) different people what their date of birth is, and show us in reality what the math says.
I'm still waiting for this video...
Will you consider to be the one who actually prove it, and makie such a video?
I think you will have 1M viewers.
I did it. Programmed randomly choosen 23 numbers out of 365 like 10000 times or more (10000 groups of 23 numbers) and calculated how many times there were atleast 2 equal numbers,and then just divided by 10000 and numbers are almost the same as exact probability.
I once met a person born the same day, the same month and the same year as myself, albeit in a different country. Oddly enough I noticed that we had fairly similar characters (although I am a man and she was a woman).
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.
It's not a paradox. It's math (or statistics to be precise)
Paradox because it is not realistic only in theory mathematically
Best indicator(s) of this are location between the "poles", cultural, religious belief systems, and species.
Many people near the equator don't have children in winter months... but conceive them during that time period or late fall. (Exception is Valentine's Day)
There are different variables connected to "why". Need/desire for survivability being important. Availability of food, the right conditions, etc...
My brother and cousin had the same b-day... not the same year. Both younger brothers and from a big extended family of religious devoted people. Ovulation cycles are another less discussed variable. "9 months of she is not available" is another indicator... families need women😅 and men know this.😊
My immediate family is an outlier, we have two sets of people born on the same day. My dad and my oldest son are both born on the same day and my youngest daughter and I are also born on the same day. I agree about the results, but there are still only at most 23 dates out of 365 which is why it seems weird on first look. If you consider it like you had 365 rooms and each had every person born on that day in it. You would not think if you randomly picked 23 people you would be more likely than not to grab two people from one room instead of 23 separate rooms.
Agree totally with the chances as calculated. However shouldn't we also be able to calculate by evaluating the number of "pairs" in the room. If you have 3 people in the room then there are 3 pairs so the chances are 3/365. If there are 4 people in the room there are 6 pairs, so the chances are 6/365.... We would continue until the number of pairs is 183. Why is this giving a different answer, what did I miss.
I think some teacher taught us the "number of pairs" version. I realized by myself that it is quite wrong. The results are close, but it is wrong. One malfunction of "pairs" is that even with 500 students, it still predicts a finite possibility that there are no birthdays in common! The correct calculation is way more complex, but it is perfect because as soon as you reach 366 students, the probability of no birthdays in common drops to exactly zero.
If we calculate those having birthdays in February for example we will have a higher probability because fertilisation happens often in spring (May for example) leading to a birth 9 months later 😊
However my bd is in May, I wonder what did my parents had in mind ?! 😳 😅😂
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".
underrated
out here cooking
Most people incorrectly think about how many people it takes for 2 of them to be more likely (> 50%) to have A specific birthday, eg Dec 27. That's not the question.
Well, at least I thought so.. If you say that's not the question, can you please say what IS the actual question??
@@_Yogi_Babu ANY two people with same MMDD. Any day, not just one specific birthday.
@@russellstyles5381ok, thanks for the clarification! So, with this, imagine if the 1st person has the bday on dec 27.
So, according to the 2 differences of the question, what would be the probability of having the same bday by case 1) a specific bday and case 2) any bday for 3 persons to have a pair?
Asking, Just to have a better clarification, if you don't mind! Thanks!
I believe that situation actually came up on "The Tonight Show-with Johnny Carson" many decades ago.
There were two people with the same birthday as myself in my class when I was in primary school 🙃
I'm more interested in what happens after we find two people having the same birthday. am I going to get cake?
Shouldn't the first calculation be 1/(365*365) because person a and person b are both randomly picked? If one was known at the beginning and the other was random 1/365 would make sense. He switched from talking about 2 randomly selected people to 1 person with a specific birthday and 1 random person with a random birthday while discussing the math.
I thought the same thing, it wasn't specified that we knew the birthday of a specific person, right?
1/365^2 would be if these two people were to have birthdays on a specific given day. But since they are just supposed to have them on the same day, then the first person sets the date, and the second has a 1/365 chance that it will be the same date. Of course, leaving aside behavioral issues, such as people being more amorous in the spring, etc.
Agree (1/365)^2
What he's doing is calculating the probability that no pair of people share a birthday. We don't know anyone's birthday in advance. We take the people in a random order and consider what each person's birthday can be so that it's different from everyone we have already considered. For the first person, nobody has been considered yet, so they can have any of the 365 birthdays available. This is a 365/365 chance. Since that is equal to 1 and multiplying by 1 doesn't change the probability, the person in the video glossed over that detail. The second person can then have any birthday besides the first person, leaving them with 364 options out of 365, and so on...
very good
Thank you!
🤔23 and me rabbit hole gets deeper and deeper....
Yes, but you're still just removing luck from the equation. It's no different than the 1000 people heads or tails paradox.
How many groups of 23 people will I have to ask what there birthday is . , before I find a matching birthday ?
You could expect to ask 2 groups. 100%/51%
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.
Uhm, if 2 share the same bd, your number goes to infinity.
As, it's possible, you have a room of 366 people - all with the same bday.
It's just as likely - right?
The answer for all is 42.
My former wife was born one hour before me. Same day, same year.
I can only say two things…
1. Given the fact a woman gives birth to a child somewhere in the world every 8 minutes the chances of meeting someone with your birthday in your lifetime is high…but low if you just randomly put 4 people in a room.
The second thing is…I think you just like yo hear your own voice and the smell of sharpies!
Here's I am trying to learn math and you put sm64 music in the background
And sms and wind waker
It's the good stuff!
When I'm trying to learn but I'm too busy jammin
Do i note a flaw? What about somebody whose birthday falls on Octember 32nd??
1/365 = 0,0027
Are we going to bring up the inclusion of February 29th? Just to throw a very small spanner in the calculation? 😂
This may seem unintuitive, but it 100% absolutely is NOT A PARADOX. PLEASE STOP CALLING IT THAT. Words matter. Definitions matter. There are many mathematical idiosyncrasies that are interesting and seem unlikely... but a statement that seems unlikely is not the same thing as a statement that contradicts itself, i.e., a paradox.
Definitions do matter. Paradox has several.
@@johnburdick3361 Nice concise response.
You draw your x backwards
veridical
What's a Paradox?
There is no one answer to that question as it depends on context. At the most literal, we may say a paradox is any statement like: P and not P. That is - something paradoxical/contradictory. In this context we're discussing what's sometimes called a 'veridical paradox', which means there isn't actually any contradiction logically, the only 'contradiction' is that the truth of the matter runs counter to our intuition, so it feels paradoxical. Often a 'paradox' is an impossible result that comes from seemingly reasonable premises, thus showing us there must be an error in our premises.
The birthday problem is a surprising and counterintuitive example, but it is NOT a ‘paradox’.
It's just called a paradox by name it isn't a paradox by the technical meaning, paradox here just means it ain't what ud think it is
jan Misali's five kinds of paradox would categorize this as "unintuitive fact"
Jan Misali is the GOAT
@@WrathofMath Hell yeah
Can anyone explain mathematicaly
leap years?
leap years makes only an insignificant change.
Except for the last question. You need 367 people in the room to be sure that no one shares a birthday.
cool
Hi . At 366 you still don't have 100% probability because of the leap years. Sorry for being a PIA but being a non-mathematician it still poked my eye.
If you use standard rounding, it reaches 99.9% at 67 rather than 75, at 99.844%, which rounds off to 99.9%
You can't say it's reached 99.9% if it's less than 99.9%, even if it rounds to 99.9%.
@@eduardoxenofonte4004 It is common practice. You seem to be specifying Trunc rounding, which is a valid algorithm.
@@russellstyles5381 Rounding before comparisons is a disingenuous practice. For example, if you round the probability to the nearest integer, you could say it reaches 100% at 23 people. Rounding should only be used for displaying values concisely.
I dont understand a single thing, i can barely remember my own birthday 😂😂
This question obviously doesn't take into account that people are born more often on certain days. Example, mid October is common because they were conceived on Valentine's Day, December 25th is very uncommon because Christian mothers will deliberately avoid that day and will have the doctors induce an early pregnancy, which bloats the chances of the proceeding days.
This is true, but it's not super relevant to the problem at hand because that only makes it more likely that a small group of people would have a common birthday. So the 23 number is a worst case scenario so to speak. Assuming uniform distributions of birthdays, it takes 23 people. Accounting for the non uniformity would only increase the odds for 23 people sharing a birthday, and accounting for leap years is an insignificant change that doesn't add anything to the interest of the problem.
Valentine’s Day conceptions are born in November, not October
@@KarlBonner1982An extremely servere case of premature ejaculation perhaps.
23hr ago 2:31
👍
A twist:
I belong to a Discord group of 20 people.
A few months ago, we discovered that I share a birthday with two of the others.
I think it's about 0.86% likely for 3 people in 20 to share a birthday. This number was greater than I expected; it's almost 1%. And for it to be more than 50%, I think it takes 75 people.
I used C(group size, 3) ÷ 365²
Did I do it correctly?
My heavens, how did you not catch the mistake before you published this video?
But i didn't see among my classmates who shares same birthday (24)
people when probabilities are probabilities
You have failed a coin toss before, right?
It's not really a paradox. And you didn't really explain it very well with the lollipop people, you didn't really explain how and why 364/365 running to 343/365 of not having the same birthday translates into 0.49. It doesn't feel intuitive to me with your negative explanation. I feel you skipped the intuitive part of that explanation.
The dots however was more intuitive for me. If I imagine a room divided into 365 squares, and I ask 23 people to throw coins into the room, then to say it's more likely than not that there will be a square with two coins in it sounds quite reasonable.
why is this a paradox?????
Clickbait.
Why can't we just do a more straight forward calculation?
As you told in the beginning,
the probabilities of persons sharing the bdays are:
1st person 0
2nd person 1/365
3rd person 2/365
.
.
.
183rd person 182/365 = 0.498
And for the 184th person 183/365 = 0.501
So, why not the min persons reqd to share the bday is 184?? - Which is just above half of the total number of days! It makes sense that way.. Ain't it?? Then, where's the issue or wrong in this??
Also, yourself mentioned that with 366 people, we can certainly say that 100% chance of finding a pair, and going by the same logic, with just more than the half of 365, should be >50%. Right??
But with 23 people, the 23rd person has a mere 22/365 app= 0.06% chance only!! 🤔 How's it correct??
So, the answer should be 184, not 23. Isn't it??
Thanks!
Each person beyond the second has a greater chance than the last to share a birthday with one of the previous people because the pool of possible birthdays that could be picked and be different is shrinking. You made the assumption that 183 people have different birthdays and the 184th person and anyone beyond that could have any birthday.
@@gamer122333444455555 Yes, in my approach too every subsequent person's addition increases the chance of getting a pair, without doubt - that's why you are witnessing the increase in the chance probability!
No assumption is made whatsoever.. The chances of getting a successful pair is what is being obtained, with every additional person! This actually means, the chances of an existing bday sharing is actually increasing - which is perfectly valid and without any assumption!
To emphasize more on this, even the 2nd person can happen to share the bday with the 1st person - but only the chances of such occurance is minimal - there's no form of assumptions, whatsoever!
To explain in very simple terms,
Minimal chance is for the 2nd person. (Just > to 0).
Maximal chance is for the 366th person. (just > to 100).
So, obviously 50% should be around the middle! (just > to 50).
Simple!
@@gamer122333444455555No assumptions were made, whatsoever! As you rightly mentioned, each subsequent person has a higher probability of matching, than his previous one - that's absolutely right and hence 2/365 is greater than 1/365 and 3/365 is greater than its previous value of 2/365 and so on..
Reg the assumptions you mentioned, 183 people weren't assumed to be distinct - but only the probability of them to have matching b'days were identified. To be honest even the 2nd person can have the same b'day as the 1st person - nothing stops it, but only the probability is very less i.e. 1/365!