What's The Probability?
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24-02-2015, 09:11 PM
RE: What's The Probability?
(24-02-2015 08:09 AM)DLJ Wrote:  Warning for Anj:
You might like the story but, yes, it's going to have a maths question in it. Sorry.

So, I've just arrived in Bangkok. I fucking love this place... everyone is sooooo friendly!

Not long before we landed the guy next to me asked to borrow my pen to fill in his immigration card.

English guy, living in Perth (where I was last week) who was coming to BKK to meet up with his mum and dad (which is why I went back to England a couple of weeks ago). So we had a bit in common (which was nice) and had a chat.

There were a few more coincidences but I won't bore you, reader, with any of that.

A little later, he asked again to borrow the pen but this time on behalf of the Chinese guy who had the window seat next to him.

The immigration form is written in English and Thai and the Chinese guy was struggling to guess some of the notes. To help, the English guy showed him his own completed card.

A look of surprise from the Chinese guy as he spotted that they shared the same birthday.

What's the chances?

At a guess, I'd say there were about 40 rows, with three seats per row each side of the aisle... maybe 240 seats about 90% occupied.

I recall reading somewhere about the fact that you only need 23 people in a room for the probability of 2 people having the same birthday becomes greater than the probability of everyone having different birth dates.

But what are the chances of those two actually being seated next to each other.

Anyway, I noticed their mirth and asked what was happening and the English guy showed me his card. I asked, "Is that a 7 or a 9?"

He obviously thought I was thinking that their birthdays were the 7th and the 9th and that this was unusual but he said, "No, look, both 09 / 02"

I must have had an unexpected reaction to that because he asked what was up.

I showed him my card.

So what, FFS, are the chances of THREE people sharing a birthday being seated next to each other on a plane.

Do AirAsia (I know, yes, I'm a risk taker) allocate seats by birth date?

We took photos of the cards (I'd upload if I knew how) and the Chinese guy took a selfie of the three of us.

Seriously, what are the chances of that?

As we stood up to disembark I was tempted to call out to everyone else to ask if there was anyone else born on that date. It's possible, I suppose, but unlikely that everyone was born on the 9th of Feb.

But how unlikely?

Huh

My son (who loves math) blithely said he would have asked the Chinese dude.

Facepalm

I know there's a high probability like 70% chance with 30 random people two or more will have the same month and day of birth.

The odds go waaaaay down if you add in year. But the odds of having the three of you randomly seated together on the same row...

That's like wow.


But as if to knock me down, reality came around
And without so much as a mere touch, cut me into little pieces

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25-02-2015, 12:15 AM
RE: What's The Probability?
(24-02-2015 09:11 PM)Momsurroundedbyboys Wrote:  The odds go waaaaay down if you add in year. But the odds of having the three of you randomly seated together on the same row...

That's like wow.

Nah, not so big deal. Coincidences happen all the time, we cherry-pick and remember the ones that seem to stand out. Sure, the probability of *that particular coincidence* happening is small, but our brains are looking for meaning and coincidence *all the time*.

We'll love you just the way you are
If you're perfect -- Alanis Morissette
(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
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25-02-2015, 05:43 AM
RE: What's The Probability?
Thanks FC, that was terrific (also terrifying!)

I'm regretting not asking all the other passengers now. Sad

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25-02-2015, 06:31 AM
RE: What's The Probability?
Quote:My son (who loves math) blithely said he would have asked the Chinese dude.

That kid is gonna go far in life MomSBB. Good job.

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25-02-2015, 08:10 AM
RE: What's The Probability?
(24-02-2015 12:48 PM)Stevil Wrote:  If you have a person to your right and one to your left then it is 2/365 which is 1/182.5

If he is on a return flight then we halve that again. 1/91.25

I don't think this is right, but I haven't taken stats in a while. The likelihood of a getting three of a kind is far less than two of kind, or just drawing any one card.

The likelihood of 3 random people having different birthdays would be, about 99.18% (365/365) * (364/365) * (363/365) = 99.18%.

So the likelihood of having the same birthday would be about 0.82%. I'm not too sure how to extend this further, by calculating the chances that all three of these individuals would be seated next to each other, given the probabilities of any given combination, but I would think it would be bordering on lottery probabilities at this point.

But like I said it's been awhile since I had to work through problems like this, so I'm sure there are folks here far more capable of doing the math than I am.

*nvm it looks like full circle did the work already.
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25-02-2015, 08:15 AM
RE: What's The Probability?
Don't forget all male too.
Blood type? Handedness? Eye color?.....
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25-02-2015, 08:20 AM
RE: What's The Probability?
A few years ago people were sandblasting our swimming pool prior to retiling it. What's the probability of getting *a* particular grain of sand in your eye? Miniscule right? But if you're not wearing safety goggles, the probability of getting *some* grain of sand in your eye is 1.

It's the same with this coincidence. Stuff happens all the time. The probability of any one configuration happening is miniscule but the probability that *something* happens is 1. And then along comes monkey with pattern recognizing brain and looks at all the things that happen, picks out the ones that seem *waaay* improbable, and says "Holy shit! Coincidence!"

Say a DNA paternity test is so accurate that the probability is 1 in a million that a match will be declared if in fact there is no match. Now it's rolled out across the world as *the* paternity test and a billion people use it. 5000 people will be incorrectly identified by this so-amazing test.

Small probabilities when amplified by large numbers of test cases result in "coincidences" that ain't so surprising Drinking Beverage

We'll love you just the way you are
If you're perfect -- Alanis Morissette
(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
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25-02-2015, 12:48 PM
RE: What's The Probability?
(25-02-2015 08:10 AM)Tomasia Wrote:  
(24-02-2015 12:48 PM)Stevil Wrote:  If you have a person to your right and one to your left then it is 2/365 which is 1/182.5

If he is on a return flight then we halve that again. 1/91.25

I don't think this is right, but I haven't taken stats in a while. The likelihood of a getting three of a kind is far less than two of kind, or just drawing any one card.
I was giving the odds of two people with same birthday sitting next to each other. The odds of three, given that you only get three seat rows is 1/365 X 1/ 365 which equals 1/133,225 then if the plane was full, you would divide that by the amount of three seat rows that are on the plane. If the plane isn't 100% full, you would need to make a statistical probability for how many three seat rows would be full.

It's not of miracle proportions given that millions of people fly, it probably happens quite often, just not quite often to me.
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27-02-2015, 10:46 PM
RE: What's The Probability?
(24-02-2015 12:42 PM)ScatteredThoughts Wrote:  I'm lazy and also suck at the maths, so I just searched a bit until I found this:

http://www.calctool.org/CALC/math/probability/birthdays

According to that tool, there is 100% chance that 2 people will have the same birthday.

**ETA**

And I see that I didn't fully read the initial post. I don't know how you would determine the chances of the people actually sitting next to each other. Interesting problem.

100% is an absolute. This is obviously a result that is based on rounding after some digit, but It much prefer it be displayed to their nearest reckoning, e.g. 99.99999 %. It is perfectly possible (theoretically) , however unlikely, that of the ~7 billion people on the planet that only one person was born on a particular day.

There is another problem with figuring this out as well; calculators and equations cannot accurately account for the true solar days. The reason why I say cannot is that each day is slightly different in length and we can only measure how different to a particular degree. Humans, for the most part, calculate our days using a 24 hour (or equivalent for systems that measure hours differently that 60 minute; 60 second systems) day. Using the Gregorian Calendar we also have leap days every four years to help keep our calendars more accurate, but that isn't completely accurate either. I predict in the relatively near future we will use "True Solar Time" and a more accurate Solar Calendar will naturally follow. While the Gregorian Calendar is a Solar Calendar, it is a lot less accurate than we have the technology to make. As internet-based clocks become the standard you will see this change. In the meantime days of birth will be occasionally wrong technically speaking from what is generally accepted.

As an anecdote I have an Uncle and cousin who share the birth date of 29 February. Big Grin

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27-02-2015, 10:51 PM
RE: What's The Probability?
(27-02-2015 10:46 PM)Dark Light Wrote:  
(24-02-2015 12:42 PM)ScatteredThoughts Wrote:  I'm lazy and also suck at the maths, so I just searched a bit until I found this:

http://www.calctool.org/CALC/math/probability/birthdays

According to that tool, there is 100% chance that 2 people will have the same birthday.

**ETA**

And I see that I didn't fully read the initial post. I don't know how you would determine the chances of the people actually sitting next to each other. Interesting problem.

100% is an absolute. This is obviously a result that is based on rounding after some digit, but It much prefer it be displayed to their nearest reckoning, e.g. 99.99999 %. It is perfectly possible (theoretically) , however unlikely, that of the ~7 billion people on the planet that only one person was born on a particular day.

There is another problem with figuring this out as well; calculators and equations cannot accurately account for the true solar days. The reason why I say cannot is that each day is slightly different in length and we can only measure how different to a particular degree. Humans, for the most part, calculate our days using a 24 hour (or equivalent for systems that measure hours differently that 60 minute; 60 second systems) day. Using the Gregorian Calendar we also have leap days every four years to help keep our calendars more accurate, but that isn't completely accurate either. I predict in the relatively near future we will use "True Solar Time" and a more accurate Solar Calendar will naturally follow. While the Gregorian Calendar is a Solar Calendar, it is a lot less accurate than we have the technology to make. As internet-based clocks become the standard you will see this change. In the meantime days of birth will be occasionally wrong technically speaking from what is generally accepted.

As an anecdote I have an Uncle and cousin who share the birth date of 29 February. Big Grin

As a kid we had babysitters who are identical twins who were born on Leap Day.

My wedding anniversary is Leap Day.

My aunt and uncle (married, not twins) were both born on July 4th.

See here they are the bruises some were self-inflicted and some showed up along the way. - JF

We're all mad here. The Cheshire Cat
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