The risks of Eggstasy

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understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Submitted by david on Thu, 04/02/2010 - 4:43pm

There has been extensive coverage of a box of 6 eggs found to be all double-yoked:an event that was given odds of a trillion to 1 against. This was based on the British Egg Information Service saying 0.1% ( 1 in 1000) eggs were double-yoked, and so getting six of these required these odds to be multiplied 6 times. In fact this gives 1 in 1,000,000,000,000,000,000, but which was reported as a trillion (now usually taken as 1,000,000,000,000).

The Daily Mail did a good demolition of this story, and it is a good example of what can go wrong when people try and work out chances.

But it also provides a fine illustration of the questions to ask when trying to deconstruct a story like this, where the uncertainties and errors can creep in at different levels.

  1. Is the number plausible? Answer – No. An extraordinary total of 11,000,000,000 eggs are eaten in the UK every year, that’s on average 1 every 2 days for every single person. That’s nearly 2,000,000,000 half-dozens, and so if this event were as rare as claimed, we would expect it to happen every 500,000,000 years, on average. even if it's a trillion to 1, it still would only happen on average every 500 years. Not plausible.
  2. Are the ‘parameters’ of the analysis right? Answer – No. The 'risk' is not the same across all boxes. Double-yokes are more common in larger eggs, and the photos clearly show the box is of extra-large eggs.
  3. Are the assumptions underlying the ‘model’ right? Answer - No. Eggs in a box are not independent events, they are likely to come from a similar batch and so once one double-yoker has been found it increases the betting odds on others being in the box.
  4. Are there ‘unknown unknowns’ we have not even thought of? Answer - Yes. Double-yokes are detectable, some branches of Waitrose even sell boxes of double-yoked eggs.

So, sadly, another probability story in the news is shown to be so much (eggy) froth.

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