# What are the chances of six double-yolkers?

• 10 December 2011
• From the section Magazine

What are the chances of finding half-a-dozen double-yolk eggs in a single box?

Last Sunday in a kitchen in suburban West London, what looked like a statistical miracle took place.

In the course of making profiteroles, two friends cracked four eggs one-by-one into a mixing bowl. The first was a double-yolker. The second, was also a double-yolker. With a sense of anticipation they crack the third - again a double yolker.

Surely not the fourth as well? As they cracked the final egg, another double-yolker fell into the mixing bowl.

What are the odds against that happening? Huge, one might suspect.

This actually happened to Jen Clarke, a colleague of the More or Less Team on Radio 4, and her friend Lynsey.

According to the British Egg Information Service, one in every thousand eggs on average is a double-yolker. They're not sure how they've come to this figure but you would like to think that the British Egg Information Service was able to supply useful information about British Eggs, so let's give them the benefit of the doubt.

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

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.

It's not as simple as that. What you have to consider is the fact that these eggs may be likely to come in clusters.

Here we need to turn to an expert. Richard Kempsey is agriculture director at Stonegate, which supplies eggs to supermarkets. He says double-yolked eggs almost always come from young hens about 20-to-28 weeks old.

"In reality it gets its mechanics just slightly wrong. You get a young bird and it comes to lay its first egg and it releases more than one egg yolk. It forms a shell around the egg and out pops a rather large egg with two egg yolks in it."

The chances of getting a double-yolk from one of these hens is much higher. One in every 100 eggs from these birds are double-yolk.

We've also learned from our research that the eggs in a box are very likely to come from the same flock, and flocks are usually around the same age. 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.

And the same goes for the third and fourth eggs. So taking all that into account lets do the sum 1000 x 100 x 100 x 100 - that equals one billion - so the probability of finding four eggs in a row in a single box is one in a billion.

A one-in-a-billion event is still pretty big, although compared to a one-in-a-trillion chance the difference is huge. A trillion is 1000 bigger than a billion and amounts to the difference between something happening once a week compared with once every 20 years.

So the event that occurred in Jen's kitchen was a billion-to-one event? Probably not. There's another big factor we need to consider - the size of the eggs. Double-yolk eggs are far more likely to be large. Yet the eggs that young birds lay are normally small.

Any large eggs that are laid would be picked out and boxed together. This means if you find a large double-yolk egg - and you know the other eggs in the box are from the same young flock - then the chance that the other eggs are also double-yolkers becomes a lot more likely. In the most extreme case, you'd find that if the first egg is a double-yolker, all the eggs are double-yolkers.

So bearing all this in mind what happened when we went back to the last two eggs in Jen's box? Well as if to prove us right it turned out egg five and egg six were both double-yolkers.

On our initial naive reading this would be a one-in-a-quintillion double-yolk streak. But as with most things there's actually a more obvious explanation

You can hear the latest edition of More or Less here.