The risks of Eggstasy
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.
- 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.
- 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.
- 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.
- 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.