The capitalist yolk

The BBC has a story about the probability of getting six double-yolked eggs in a box of six.  It points out that young hens are more likely to lay double-yolked eggs, and those eggs are larger than normal, so if you buy a box of large eggs which happen to have been selected from eggs laid by young hens, the odds of their all being double-yolked are much shorter than the one in a million trillion they first thought of.

Well yes, but the odds must still be pretty long.  And there have been other similar stories, not least this one about a woman who opened 29 double-yolked eggs in a row from a box of 30.

When something wildly improbable seems to have happened, it's as well to consider alternative explanations.  Here's a clue from David Spiegelhalter, Professor of the Public Understanding of Risk, who was intrigued to find he could buy a box of double-yolked eggs from Waitrose: he mentions it in this article.

It turns out that double-yolked eggs can be identified easily enough by shining a light through them - "egg candling".  (It's safe to try this at home.)  Egg producers operate egg-grading machines: I suppose the machines include automated candlers as part of the grading process.  So it's not unlikely that some machines automatically separate double-yolked eggs. Some of those eggs will be sold as such for a premium, if demand exists.  And if the demand is less than the number of double-yolked eggs produced, they'll just get put into regular boxes for the appropriate size of egg.  I reckon the odds of this happening sometimes would be very close to one.