This whole thing started last week when I cracked open an egg and two yolks fell out. I couldn’t believe it. Maybe a month prior to this magical incident, I had asked a group of 10 of my best friends from college if they had ever cracked “twin yolks” to find out that, like me, most of them never had. But how likely is it actually to crack twin yolks? I had to explore.
I naturally went to Google and quickly found that the odds of any individual egg having double yolks is 1 in 1,000, according to eggsafety.com. That’s pretty unlikely, although far more common than I had expected. But then, something amazing happened.
What are the odds of getting two twin-yolk eggs in one dozen?
Later in the week, I cracked another egg from the same dozen and found yet another twin yolk. Now my mind was really blown. Two out of 12 eggs are double-yolks!? that must be like a 1 in a million chance, right?
Well, no. Simple math tells us that the odds of getting an egg with two yolks in a dozen-egg carton is about 1 in 84. That means that the odds of getting two eggs with double yolks in the same dozen-egg carton is 1 in 15,303.
In all, my 12-egg carton ended up having five eggs with twin-yolks. Now, the odds of that are stupid. That’s not supposed to happen, so I did some more research and as it turns out, I’m not the only one who has had some amazing egg cartons.
What are the chances of getting 12 double-yolk eggs in a dozen?
|Number of Eggs Having Twin Yolks||The Chances of That Happening in a Dozen|
|1 twin yolk egg in a dozen||1 in 84|
|2 twin yolks||1 in 15,303|
|3 twin yolks||1 in 4,586,569|
|4 twin yolks||1 in 2,036,436,607|
|5 twin yolks||1 in 1,271,000,000,000|
|6 twin yolks||1 in 1,088,000,000,000,000|
|7 twin yolks||1 in 1.27E+18|
|8 twin yolks||1 in 2.03E+21|
|9 twin yolks||1 in 4.56E+24|
|10 twin yolks||1 in 1.52E+28|
|11 twin yolks||1 in 8.34E+31|
|12 twin yolks||1 in 1.00E+36|
As it turns out, it more common for young hens to lay double-yolk eggs – some unconfirmed sources even cite it being as common as 1 in 30. Moreover, a single carton of eggs tends to come from the same flock, so it’s reasonable to assume that if you have a carton of jumbo sized eggs, and the first egg cracked is a double yolk, they rest of the eggs also likely came from a young flock of hens. If all of your jumbo eggs were produced by young hens, it becomes much more likely that you’ll follow that up with some more.
So, let’s say that the odds of the first egg being a twin yolk are actually 1 in 1,000. But then knowing that you have a twin yolk means that you likely will have more, so the odds thereafter are 1 in 30. This is what the actual binomial distribution would look like:
|Number of Eggs Having Twin Yolks||The Chances of That Happening in a Dozen, Assuming a Young Flock After First Twin Egg|
|1 twin yolk egg in a dozen||1 in 122|
|2 twin yolks||1 in 323|
|3 twin yolks||1 in 1,871|
|4 twin yolks||1 in 18,082|
|5 twin yolks||1 in 262,200|
|6 twin yolks||1 in 5,431,280|
|7 twin yolks||1 in 157,507,131|
|8 twin yolks||1 in 6,394,789,511|
|9 twin yolks||1 in 3.71E+11|
|10 twin yolks||1 in 3.23E+13|
|11 twin yolks||1 in 4.68E+15|
|12 twin yolks||1 in 1.49E+18|