## Way More Than a Dozen

My husband and I live in Monterrey, Mexico, most of the time, not that has anything to do with the story – per se.

Two months ago, we bought an 18-pack of eggs from our local grocery store. Regular store with regular eggs, or so we thought. Over the years, I have cracked an egg and have been surprised to see two yolks, or even a little red spot. So, when I cracked the first egg from the carton and saw two yolks, I wasn’t as surprised as much as I was amused. Then I cracked a second egg and there were two yolks. OK, I thought, what are the odds of that happening? The third, fourth, and fifth eggs also had two yolks. Now I know the odds are getting larger.My husband wasn’t quite sure I was telling the truth, maybe miscounting? I had hardboiled three eggs to make tuna salad, so I had my husband stand there while I peeled and opened the eggs. Yep, two yolks in all three. We are now at 8 eggs with double yolks from a pack of 18. As it turned out, there were actually 14 out of the 18 eggs that had double yolks.

We are “guessing”  they all came from the same chicken, but really, what are the odds of having that many double yolked eggs?  We will wait to see what you all come up with.

Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 206. Take a look and leave your comments below.

[This] story is more interesting, maybe because I can actually calculate the odds of this happening–with a caveat. First I’ll explain the odds, then the caveat.
I consulted several internet sources and found the information pretty consistent, so I think it’s reliable. The odds of a double-yolk are 1 in 1,000 (.001). So, if these eggs were randomly selected, the odds of getting at least one double-yolked egg in a carton of 18 are 18 in 1,000. Once one has been removed, the probability of at least one of the remaining eggs being double-yolked is .017, and so on. All told, if these eggs were randomly selected, the probability of at least 14 double-yolked eggs in a carton of 18 is .000000000000000000000000000267 (there are 27 zeros).
Now the caveat: because they all came from the same carton, it’s highly likely that they share some factors that matter, so the odds of a second egg being a double-yolker are actually dependent on whether the first is. Perhaps they all came from the same hen or they were from hens which were housed near each other and exposed to the same environment, food, and other treatments. What’s more, the hens that laid these eggs may be around the same age, and young hens are the ones that lay nearly all of the double-yolkers. So, the odds that an egg from a hen that is 20-28 weeks old is double-yolked are about 10 times greater than if the egg were chosen at random.
Because we don’t know the source of the eggs for certain, it is difficult to calculate the real odds in this case. It may be as much as 10 times greater than if the eggs were randomly selected. However, at .0000000000000000000000000267 (that’s 25 zeros) that’s still rather impressive, don’t you think?