Dealt with pretty well here:

Take a wonderfully trivial example: last month it was reported that a shopper had bought a box of six eggs, and all had double-yolks — a “one-in-a-trillion chance”. This calculation was explained on Today by a man from the Egg Council who said that, as one in 1,000 eggs were double-yolkers, the chance of all six being double-yolkers was one in 1,000 x 1,000 x 1,000 x 1,000 x 1,000 x 1,000.

This aroused my suspicion. To begin with, this is not a trillion and, if this were the true chance, we would expect to wait 500 million years before this event occurred. So what has gone wrong with this model? It turns out that the egg-world may not be so simple. Double-yolkers are far more common in certain flocks, so there should be uncertainty about the “one in 1,000” parameter. Eggs in a box tend to come from the same source so once one double-yolker is found the chances increase that the rest will match. As a result there is uncertainty about the structure of the model too.

Acknowledgement of parameter and structural uncertainty has become common in climate and other models. But there is a further level of uncertainty: of unforeseen surprises, Black Swans and Rumsfeldian unknown unknowns. There should always be a suspicion that there’s more going on than we can express in mathematics. Indeed, at Waitrose I bought a box marked “double-yolked eggs” for £2.49. Certainly not a one-in-a-trillion chance: double-yolked eggs can be common and can be detected, selected and packed at will.

Via http://understandinguncertainty.org/blog/6?page=1

Richard Dawkins deals with this kind of thing - our perception of coincidences - and more in his best book, "Unweaving the Rainbow":
http://www.amazon.co.uk/Unweaving-Rainbow-Science-Delusion-Appetite/dp/0...

if the stats of putting each egg in the box *were* independent, and if double yolks *were* rare (e.g. 1 in 1000), then the combined odds of 6 in a row would indeed be pretty unusual. So it's not really about his perception of coincidences. It's about how likely a box actually is to contain 6 double yolked eggs.

Keefus' question is sensible, imo. Implicit in it is the question of whether seeing 3 in a row has now made it more or less likely that he'll see a full 6. In "O Level" textbook stats, based on completely independent events, seeing 3 (or even 5) makes no difference to the overall final answer.

In the human world we live in though, other factors are relevant. They don't mean stats is bogus-they mean that it has to be used extremely carefully (c.f. the blog I quoted).

For all the human reasons cited in Prof Spiegelalter's blog I'd agree wqith him that seeing 3 in a row *in this context* may well suggest that the chances of a full box are quite high. My street-smart FPO however reckons that the chances are actually lower than random, because most of the double yolkers have already been nabbed for the special boxes-they should weigh more ? Perhaps K will find he has a box of 5. It was meant to be a box of 6 and failed it's final QC check ;-)

Have you checked the rest yet?

...boxes of double yoke eggs, so it's definitely occurred before. Pass an egg in front of a strong light source and you can check...Perhaps you have the product of a bored egg-checker?

or a Hens Egg Trick?

described an egg as a perfectly packaged chicken period, enjoy your double yokers!

Another double yolker.

Thanks for the stats links; I haven't got the maths to follow it all but I think I get the gist.

Regarding the "randomness" of the eggs, the box was branded "Very Large Free Range", so I think there's two factors increasing the likelihood - if they're chosen by weight, double yolkers are heavier; and maybe free range hens tend to lay more double yolks?

Anyway, watch this space. I might have an omlette tonight...

... another double.

I'm unfeasibly eggcited now.

All six now. Is there someone I should notify?