You must be yolking...

December 10, 2011 4:15 AM

"So, if the probability of finding an egg with two yolks is 1/1000 - then to find the likelihood of discovering four in a row you simply multiply the probabilities together four times. One thousand to the power of four brings us to the grand total of one trillion...

If true that would mean the event that occurred in Jen's kitchen was a trillion-to-one event. But is it true? No is the short answer."
posted by Petrot (38 comments total)

What are the chances of that? Huge, one might suspect.

Actually, one might suspect the chances of that are rather small.
posted by spaceman_spiff at 4:22 AM on December 10, 2011 [8 favorites]

On that basis we can say that while chance of finding one double-yolk egg may be 1/1000, the chance of finding a second is considerably higher - more like 1/100.

I can only hope the afterlife awaiting whoever derived this conclusion somehow involves Monty Hall.
posted by 7segment at 4:25 AM on December 10, 2011 [7 favorites]

Huh. On two occasions in the last couple of years I've had four or five eggs out six (as in I bought six eggs) have double yolks, so it never occurred to me that it might be considered to be some hugely unlikely thing. On the contrary.

These weren't large eggs, though – more like medium-small... and brown, as most eggs here are.
posted by taz at 4:38 AM on December 10, 2011

If you were to look through 1000 eggs of *all* sizes, you might find only 1 double yolker, but in a carton of larger sized eggs (in Australia, the largest I know of is called Jumbo, it's larger than XL; a dozen weighs 800g) double yolkers are very common.

If I buy a carton of Jumbo eggs, it's not at all uncommon for me to see two double yolker eggs. I've never seen three in a carton, and I often see none.
posted by surenoproblem at 4:38 AM on December 10, 2011

> > On that basis we can say that while chance of finding one double-yolk egg may be 1/1000, the chance of finding a second is considerably higher - more like 1/100.

> I can only hope the afterlife awaiting whoever derived this conclusion somehow involves Monty Hall.

Well, that certainly makes sense if the conditions are such that some chickens lay more double-yolkers than others and the eggs from one chicken tend to stay close to each other throughout the pipeline -- thus the first double-yolker is an indication that the eggs in front of you are more likely than most to have come from a chicken that lays more double-yolkers than most.

That aside, I can imagine Hell for a statistician to be an endless repetition of a version of Monty Hall where even the host himself does not know where the goat is but everyone around you still insists that switching doors makes a difference.
posted by Anything at 4:58 AM on December 10, 2011 [3 favorites]

They also neglect the fact that Binomial(12,4) = 495, which means there's 495 different ways you could choose 4 eggs out of a dozen. Even if there was no covariance on account of eggs in a carton coming from the same hens, and the chance of a double yolk of any egg was a straight 1/1000 as in the opening premise, the chance of picking any 4 out of a dozen and finding all double yolks would be 1 in 2 billion, not 1 in a trillion.
posted by Rhomboid at 5:01 AM on December 10, 2011 [2 favorites]

The probabilities, relevant scientific input, statistical analysis, econometric modeling, and ensuing discussion are of interest mainly to eggheads.
posted by twoleftfeet at 5:02 AM on December 10, 2011 [7 favorites]

They also neglect the fact that Binomial(12,4) = 495, which means there's 495 different ways you could choose 4 eggs out of a dozen.

I am pretty sure it was a six-egg carton.
posted by GenjiandProust at 5:03 AM on December 10, 2011 [1 favorite]

Oh, and by the birthday theorem there is a 1.2 percent chance (or about 1 in 84) of buying a dozen eggs and finding at least one double yolk.
posted by Rhomboid at 5:06 AM on December 10, 2011 [2 favorites]

Okay, Mr Smartypants, now tell me how likely it is that in Recents Comments, I see this:

Yolks can be good?

followed directly by

You must be yolking...

Totally serious, and I didn't recently comment on the Ask Me question to make this happen on purpose.

I even get double yolks on Metafilter... I'm like the yolk whisperer or something.
posted by taz at 5:48 AM on December 10, 2011 [4 favorites]

I have a hen that sometimes lays double-yolkers, but with this girl you know it right away. These eggs are huge. You can't close the carton over them. She laid two in two days once, and we were a combination of amazed and worried. We worried about what passing two giant ones in row like that were going to do to the girl. So if you get a dozen from us, it's not uncommon to get a double yolk or two.
posted by azpenguin at 6:15 AM on December 10, 2011

I used to live next door to an egg-producing farm; they used to give our family a couple dozen double-yolkers a week, plus of course use a lot themselves. Apparently double-yolks aren't nearly as rare as most folks think; it's just that the commercial farms try to pull them, because a lot of people don't like them and therefore co-ops (like our neighbor's) preferred not to receive them.
posted by easily confused at 6:25 AM on December 10, 2011

quadruple yolker!
posted by surenoproblem at 6:28 AM on December 10, 2011 [1 favorite]

That could have been a great investigation into all the fantastically complex ways items are intercorrelated. It is very difficult to get truly random samplings even if you know the population distribution perfectly. Unfortunately they stopped at the 1/100 number and didn't investigate any further.
posted by benzenedream at 6:28 AM on December 10, 2011

What is the probability that this morning I cracked two eggs and got two double-yolks and also that the top article on MeFi would be about double-yolk eggs? Yes, this just happened.
posted by sixohsix at 6:31 AM on December 10, 2011 [4 favorites]

Oh, and by the birthday theorem there is a 1.2 percent chance (or about 1 in 84) of buying a dozen eggs and finding at least one double yolk.

That's not the birthday theorem.
posted by escabeche at 6:44 AM on December 10, 2011

What is the probability that this morning I cracked two eggs and got two double-yolks and also that the top article on MeFi would be about double-yolk eggs? Yes, this just happened.

Then the answer is 1.
posted by escabeche at 6:44 AM on December 10, 2011 [11 favorites]

I drove to the grocery store this morning and saw the license plate ARW-357. Can you believe that? The probability of me seeing that particular license plate is so low, that I was freaking out. Luckily, when I got home, there was an FPP on MeFi talking about probability, so I could just share my amazing story there.
posted by King Bee at 6:47 AM on December 10, 2011 [5 favorites]

Once, when I was about 20 years old, my girlfriend and I were at her apartment making eggs for breakfast. It was a fresh carton of one dozen eggs. The first few eggs we cracked were all double-yolks. I insisted that we had to crack every single egg in the carton, and I had to promise that I would eat all the eggs before she would agree.

Eleven out of the twelve eggs were double-yolked. I used her camera to take a picture of the eggs, and then I scrambled them and ate them and didn't feel super hot.

A few years after we broke up, I asked if she still had that picture of the double-yolk eggs. Unfortunately, she had destroyed it when she purged her life of everything that reminded her of me.

Anyway. According to Wikipedia, double-yolk eggs can occur when ovulation occurs too rapidly. What's more, growers use lighting programs to stimulate egg production. It doesn't seem like too much of a stretch to believe that an overstimulated flock could produce an unusually high number of double-yolk eggs.
posted by compartment at 7:09 AM on December 10, 2011 [2 favorites]

I have never seen a double-yolk egg.
posted by mr_crash_davis at 7:12 AM on December 10, 2011 [1 favorite]

I was making macarons, which is an egg white and almond flour cookie. Every egg I cracked was double yolk. Which was quite annoying, actually. Although I did make a yummy custard, so it all worked out. That said, jumbo local eggs seem to have a much bigger chance of double yolks.
posted by dejah420 at 8:25 AM on December 10, 2011

So...where can I get these double-yolked eggs? *wipes drool off mouth*
posted by Alnedra at 8:26 AM on December 10, 2011 [1 favorite]

There is a restaurant in the Chicago suburbs that only serves double yolk eggs. I think the name of the place is Elly's.
posted by k8lin at 9:04 AM on December 10, 2011

I am a statistician. My idea of hell is being forced to play the lottery (in games where there's no rollover, so my expected winnings are negative) while listening to sports announcers blather on and on about what has or has not happened in ridiculously small samples.
posted by madcaptenor at 9:09 AM on December 10, 2011 [6 favorites]

There is a restaurant in the Chicago suburbs that only serves double yolk eggs.

Now I'm envisioning a restaurant, that no matter what you order, they give you a double yolk egg. It's a little like this.
posted by King Bee at 9:45 AM on December 10, 2011

This kind of mistake ends up in people going to prison.

Angela Cannings was sentenced to life in prison after three of her children died young of unspecified causes (SIDS), they died over the course of a 10 year period, all at about the same age.

It was the opinion of Professor Sir Roy Meadow, a man of whom I have no opinion high enough not to constitute libel, that the chances of this happening by accident were vanishingly low. Of course, the esteemed professor didn't understand the difference between conditional and unconditional probability.

If there is a genetic component to SIDS (which is likely), or an environmental one (also likely), then the chances of multiple such deaths from the same parents is actually much higher.
posted by atrazine at 10:40 AM on December 10, 2011 [3 favorites]

In addition to the exciting statistical issues I want to publicly acknowledge how delightful I find the word 'double-yolker'.

Double-yolker.

Double-yolker!
posted by Anything at 11:20 AM on December 10, 2011 [2 favorites]

It should also be the name of some maneuver in competitive gymnastics.
posted by Anything at 11:24 AM on December 10, 2011 [1 favorite]

It's funny that the article makes it seem like trillion-to-one events are miraculous in some way. They're not. You can construct a trilloin-to-one event quite easily in the comfort of your own home if you live in a big city. Take out your phone book and pick a name randomly. Then call that person and tell that person to do the same. The odds of the second person and the third person being rung is 1 in a trillion.
posted by storybored at 12:21 PM on December 10, 2011 [1 favorite]

This is a great illustration of how probability breaks down when randomness isn't the driving force behind outcomes.

I heard an interview with a wildcard pick from this year's US Open tennis tournament where he assessed his chances of taking home the title as '1/128--not bad odds!' And of course I just shook my head and thought how that makes the past 10 years of men's tennis results a statistical anomaly beyond all comprehension. Federer and Nadal are two amazingly lucky men. No skill, of course. Just luck.
posted by yellowcandy at 12:46 PM on December 10, 2011 [3 favorites]

In the name of science and posterity: only a couple months ago we had a carton of jumbo eggs where every single one was double-yolked. Given how chickens are raised and treated, I wasn't very surprised, though I have yet to reencounter the phenomenon. It seems like we ought to be able to get the Chicken Little of eggs going before we get Chicken Little itself.
posted by chortly at 12:49 PM on December 10, 2011

i sometimes buy a local farm's jumbo eggs at a locally owned supermarket and jumbo eggs are common - anywhere from 2 to 10 in a dozen, although the lower numbers are more likely

i just went to that store an hour ago and could have bought myself some more

just not impressed with this
posted by pyramid termite at 5:29 PM on December 10, 2011

You can get all sorts of weird eggs. When the girls begin laying eggs, it takes their systems a couple weeks to normalize the process. Rookie layers can lay multiple yolkers, no-yolkers ("fart eggs"), tiny complete shelled eggs inside of a second larger, hollow shell, or eggs that are entirely shell-less, like a water balloon in that thin membrane.

Very very rarely, double-yolkers can be incubated to full term and hatch successfully.
posted by Lou Stuells at 9:30 PM on December 10, 2011

that's the new-school US-style trillion with 12 zeroes.

Did I miss something here?
posted by wallabear at 11:06 PM on December 10, 2011

The British used to have 10^6 = "million", 10^9 = "milliard", 10^12 = "billion", 10^15 = "billiard", 10^18 = "trillion" and so on. Essentially the words alternate between the words most Americans know ending in -illion (for powers of 10^6) and words ending in -illiard.

I've always thought that this system is potentially confusing because "billiard" has other meanings.

Wikipedia has more.
posted by madcaptenor at 11:21 PM on December 10, 2011

We all worship at the altar of Bayesian knowledge.
posted by spitefulcrow at 1:21 PM on December 11, 2011

Thank you for that, I'd never heard of this system.
posted by wallabear at 11:54 PM on December 11, 2011

madcaptenor: "The British used to have 10^6 = "million", 10^9 = "milliard","

Related: recent Economist blog post about milliards and such.
posted by Chrysostom at 12:01 PM on December 14, 2011