What are the chances of cracking open three double yolk (chicken) eggs in a row? A cursory Internet search suggests that about 1 in 1000 eggs has a double yolk. One might naively calculate the odds of three double yolks in a row as 1/1000 x 1/1000 x 1/1000 = one in a billion.
I actually did open three double yolk eggs in a row not too long ago. Some facts that might be relevant: They were an obscure brand and they are usually out of stock at the store I go to. They are much cheaper than any other brand. That probably explains why they are usually out of stock. They only come in jumbo size. They are the only jumbo eggs the store sells. I have seen double yolks in these eggs before. I brought this up because the distribution of double yolk eggs in the population of all eggs may not be random.
I assert that since the event (three double yolks in a row) has already occurred then the chance of this happening is 100%. But suppose we could travel back in time. There’s a whole ‘nother recent thread about this. At the moment the first double yolk egg is discovered but before the second egg was opened can we apply Bayes’ Theorem to calculate the chance that the second egg has a double yolk? Similarly, at the moment the second double yolk egg is discovered but before the third egg was opened can we apply Bayes’ Theorem to calculate the chance the third egg has a double yolk? Let us continue with the assumption that one in 1000 eggs of all eggs is double yolk because 1000 is such a nice, even number.
Please do not derail this thread with suggestions on examining eggs prior to opening using techniques such as density determination, candling, etc. I really just wanted to talk about Bayes’ Theorem. On second thought, never mind. Let’s talk all about egg examination techniques, USDA egg grades, conditions on commercial poultry farms, chickens bred especially for egg production, special diets for laying hens, etc. if you want to.
Bayes’ theroem is very much using posterior observation to modify the next prediction. Obviously, finding a string of double yokes is going to change future predictions very much toward a high expectation of occurrence even if you start with a very low expectation.
A huge issue here is collecting the prior information you need to get an accurate chance.
The thing is, finding more than one double egg in a dozen is actually quite common, as eggs from the same chicken are often packed together, and they tend to all be laid around the same time.
As such, it would seem that finding one double yolk would significantly increase the chance that there will be a second one in said carton, and that finding two would increase it much more.
You’d also likely want the information about how many previous eggs from said carton were not double yolks.
Actually using Bayesian reasoning isn’t the hard part: it’s really just a formula you can apply (though it’s good to understand why said formula works). It’s determining the priors that makes it difficult to discover the odds.
We’d basically need data on everyone who finds double yolk eggs, and then also group by brand and size. Though, of course, we can use imperfect information about these to get a ballpark answer–e.g. just maybe how many double yolk eggs are found and how many eggs a chicken lays in a particular time.
You drew a completely incorrect conclusion based on a faulty understanding of statistics and poultry science. Do you have any enemies who would like to see you with
egg on your face?
(Seriously, thinking the chances of three double-yolk eggs in one carton is one in a billion is a bit like saying, “Only one in a thousand people have the last name Dorkness, but there are four of us living under one roof–that’s a one in a trillion coincidence!”)
I buy JUMBO eggs for our pets (each morning I cook two jumbo eggs for dogs, parakeets, and parrot). I’ve had two double yolks in a row too often to count, but have never had three.
Chickens lay roughly one egg per day. If anything this would tend to mean that eggs in a dozen box will come from different chickens.
If they were free range chickens and there was no control on where the chickens laid, there might be a cluster of eggs found that all came from the same chicken laid on consecutive days. This isn’t a happy answer as is suggests that some eggs could be quite old before they are collected.
You could suggest some sort of external trigger that predisposes chickens to lay a double yolk. Temperature, feed, whatever. That would get you into Bayes’ Theorem territory.
ETA - a quick search suggests that double yolk production is related to the chicken’s age, with both immature and ageing chickens more likely to produce a double yolk. So the age of a flock matters, and thus there is a causal link. Thus Bayes’ Theorem might usefully apply.
Thanks. I misremembered the explanation for why double-yolk eggs tend to cluster together. I was wondering why I hadn’t really heard of chickens laying more than one egg per day. The issue being at the flock level makes a lot more sense.
I’ve had as many as six of the dozen be double-yolks, and I could swear there was a thread here where somebody had the entire carton double-yolked. (And not from a carton of specifically double tolled eggs.)
So if you’re up for a challenge we could probably get a pretty good answer if you started keeping track of how many of your eggs each morning are double yolked and how often you get two in the same carton.
ETA:
Quick googling found the following:
Double-yolked eggs also tend to be very large. They are usually graded ‘Super Jumbo.’ Eggs identified as Super Jumbo are too large for our packing machine to pack into cartons, so they are moved to the hand packing station. At Pete & Gerry’s, these eggs are still labeled as Jumbos, even though they are technically Super Jumbos. As our team fills Jumbo egg cartons with the Super Jumbo eggs, of which more than 50% of which will include an extra yolk, that makes something fairly rare in nature suddenly appear rather common.
So the chance may be as high as 1/8 times the probability of getting a super Jumbo carton.
A guy who did a lot of flying went to a statistician to calculate the odd of being on the same plane as a bomb. After some research the statistician told him to relax, “The odds of being on the same plane as a bomb is 10,000 to 1.”
“That may sound like long odds but I fly a lot. Is there anything I can do to increase them.”
The statistician shrugged. “Bring your own bomb aboard. The odds of being on an airplane with two bombs is 100,000,000 to 1.”
Some time ago I cracked 3 eggs into a pan and each one had a double yolk. I thought it was special enough to take a photo (which I will look for and post in this thread if I can find it).
When I was a kid in the '50s, we got free-range chickens and eggs from a local farmer. Double- (and even triple-) yoke eggs were very common, and it wouldn’t surprise me if we had three in a row.
I’m not sure I understand the OP? Are you asking if we can apply Bayes’ Theorem naively to calculate the probability? (Yes.) Are you asking if we can apply Bayes’ Theorem to update our probability estimate? (Yes.) Are you tasking us with actually performing the maths? (No one seems inclined so far, possibly due to the vagueness of the OP.)
A few days is not “quite old” for eggs. People have this misconception that eggs go bad instantly the moment they’re not refrigerated, and it’s far from the truth. I think folks get that misconception because when eggs do (eventually, after a very long time) go bad, they can go very bad.
Isn’t this more of a Poisson distribution question and not a Bayesian probability?
I’m having a hard time coming up with the condition p(double yolk | ???)
If your prior assumption is that double yolks are a one-in-million, and you find two double yolks in a carton, you should update your priors. The problem is knowing how to update them. Are double yolks normally distrubuted on a curve? Or is the original probability estimate completely wrong? Is there a hidden variable affecting probability (chicken age, type and amount of feeding, whatever?)
At the very least, re-evaluating your priors should cause you to raise the probability of finding another double yolk in the same batch, or from the same supplier, or should cast doubt on the original probability estimate. Re-adjust your priors as move evidence appears as you crack more eggs. Don’t get married to an assumption.