The Birthday Paradox - let's test it

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Zuljin said:
It's not a paradox.
1. Leaving out the year opens the field a lot. Life expectancy is somewhere around 72 years.
2. About 350,000 people are born each day.
3. It's not about just my birthday. It's about each birthday in the group.

There are a fixed number of calendar days to be shared by an increasing number of people, which is well above that fixed number. There will be repeats.
Click to expand...

paradox - a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true

Seems to fit. Besides, I didn't name it.

And I think you're missing the point here. Of course people share birthdays. This has nothing to do with population or life expectancy....just pure math. You could change the game from birthdays to any other measurable item, but any logical thinker would expect the number to be much higher than 57 before you're guaranteed a duplicate. If I told you there were 365 different words written on strips of paper in a hat and you pulled one at a time, wrote down the word and put the paper back in the hat, wouldn't you think the chances of you pulling the same word twice within the first 16 are pretty small?

Because that's what we did here. In fact, we've now hit 3 duplicates in 39 people. And that's before we even have a date for every month (still missing May and July). Rough calculations (it's early) put this probability at around 7%.
 
In Middle school in a class of about 40 I shared a birthday with one of the other students. I don't know if there was another duplicated. I'd heard of this before (birthday paradox - or coincidence?) but hadn't seen the reasoning until I read your 2nd post, and that makes perfect sense. A similar, albeit easier on the math, problem would be the number of standard dice needed to get a 50% chance of rolling a 6. It is 4 (5/6 = odds of not getting a 6 on one, with 3 it is 5/6*5/6*5/6*/6 =about.48 so 1-.48 =52% of getting a 6 with 4 dice. It is almost as good at 3 dice with 43% odds.)
 
Zuljin said:
10/19

It's not a paradox.
1. Leaving out the year opens the field a lot. Life expectancy is somewhere around 72 years.
2. About 350,000 people are born each day.
3. It's not about just my birthday. It's about each birthday in the group.

There are a fixed number of calendar days to be shared by an increasing number of people, which is well above that fixed number. There will be repeats.
Click to expand...

No, MagicMatt has done it correctly, and his math is right. Year doesn't matter, just as if you have a random group of people you aren't trying to control for year.

Now, that said, what we're doing here isn't really random; we don't know how many people scan the thread and either do or don't post based on whether their birthday is listed or not. My birthday isn't listed so I'm not going to post it. There. :)

While it isn't a random sample nor a perfect test, that doesn't take away from the fact that MagicMatt is correct. <college professor here, who happens to teach statistics> :)
 
MagicMatt said:
paradox - a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true

Seems to fit. Besides, I didn't name it.

And I think you're missing the point here. Of course people share birthdays. This has nothing to do with population or life expectancy....just pure math. You could change the game from birthdays to any other measurable item, but any logical thinker would expect the number to be much higher than 57 before you're guaranteed a duplicate. If I told you there were 365 different words written on strips of paper in a hat and you pulled one at a time, wrote down the word and put the paper back in the hat, wouldn't you think the chances of you pulling the same word twice within the first 16 are pretty small?

Because that's what we did here. In fact, we've now hit 3 duplicates in 39 people. And that's before we even have a date for every month (still missing May and July).
Click to expand...

I know you didn't name it. It'd be named the Birthday McBirthday Face if someone on the internet named it.

My beef is with it being called a paradox. A logical thinker wouldn't think that because it'd be illogical. The math itself shows that. The whole premise is that this is logical. It's a thing one might not expect at first blush but makes sense after some thought, but it's not a paradox.

Out of more than six billion people, we're testing to see if a number of them share a very finite commonality; were more than one of them born on one of 365 days, and it's not even a preference. It's not something we could change our minds about due to external or internal influences. I was born the day my body came out of someone else's body. That's it. It's a done deal. And it's to see if one person will share a birthday with at least one other. It's not to see if two people were born on one specific day, say, 1/1/84. No, it's to see if any day, regardless of year, is shared. The constraints are very loose. That's another reason it works like it does. The whole thing is set up to work like it does. That is not a paradox.

But we don't have to rely on me. There are websites after websites which explain why this is not a paradox.

In the interest or intellectual integrity, I must say, debunking so called paradoxes is a game for me. I like to find the flaw, the suspension or leap of "logic", or word play, that makes facts or logical thoughts seem like paradoxes.
 
mongoose33 said:
No, MagicMatt has done it correctly, and his math is right. Year doesn't matter, just as if you have a random group of people you aren't trying to control for year.

Now, that said, what we're doing here isn't really random; we don't know how many people scan the thread and either do or don't post based on whether their birthday is listed or not. My birthday isn't listed so I'm not going to post it. There. :)

While it isn't a random sample nor a perfect test, that doesn't take away from the fact that MagicMatt is correct. <college professor here, who happens to teach statistics> :)
Click to expand...

Of course he's correct. The math is correct. We're seeing it happen... Or are we? Him being correct or not isn't my issue. My issue is with it being called a paradox.

So, are we seeing it happen? Well, we've already covered that it's not a preference issue, but what about honesty? One or more people not posting doesn't affect this. They just don't exist in the thread, but the still exist, and with birthdays. So, their birthday still applies to the situation. What can mess with it is someone saying their birthday matches just to see it come true. But, we can ignore that. We can just run the math since we know all the numbers involved. See? No paradox.
 
December 11th

Now get this... My wife and I share the same birthday but I'm two years older. Our youngest daughter's birthday is December 10th (born at 11:44pm). My oldest daughter gets her own birthday but shares it with her cousin (February 9th). LOL What are the odds???
 
Zuljin said:
Out of more than six billion people, we're testing to see if a number of them share a very finite commonality; were more than one of them born on one of 365 days,...
Click to expand...

But again, that's not correct. It's not "out of more than six billion people", it's out of 23 (or 57 depending on which point you're trying to hit). This situation doesn't take into account the population, as it has no bearing here. If there were only 57 people in the whole world, the situation still holds true that two of them are almost guaranteed (>99%) to have the same birthday.


Anyways, we just hit 60 people and have 8 duplicates already. Didn't think it would have happened so quickly, and especially not 8 times over before even making it 20% of the way to 365. Now I'm curious as to how many people it would take before every day is accounted for.

And still no May dates!
 
Hell - my immediate family is a sample size of 5, and my Dad and one of my Sisters share the same birthday - 3/13.
 

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