| Original Article on BBC website
- They got a box of normal eggs and wow the first 4 they broke were all double yolkers
- Wow what's the odds of that ?
- Well since they say 1 in 1000 eggs are double-yolkers then surely the odds are 1000x1000x1000x1000 (That's where he should have stopped ..WHY ?)
-then he said well actually in younger flocks the odds are 1 in 100 so it's 100x100x100x100
- then they opened the 5th " it's a double" ..and then the 6th " it's a double"
- I'd like to say I worked out straight away, but I didn't. I have learnt this ability to when something strange happens to just suspend belief not rush to a conclusion. So when I watch the conjurer Derren Brown I don't really try to work it all out, I just accept it. Many hours later I often suddenly realise "ah that's how he probably did it that's a ridiculously simple trick". If the trick is similar to another previous one I can sometimes see it straight away.
- In the egg case I just let it pass ..What I did realise was that it's a case of “too incredible to be true” ..so there's something going on
and then 30 minutes later I got a tweet david Spiegelhalter rather unsportingly pointed he'd debunked this already.. The article didn't give the answer straight, but pointed that it wasn't straight line thinking ..and then a Google found a comment mentioning that since there double yolk packing lines and suggested they'd run out of special boxes and so used a normal box.
- STOP.. rewind ..of course the problem is assumptions and jumping to conclusions. Yes in the whole of egg totality double-yolkers are 1 in 1000, in 1 in 100 in farms with only young hens, but it's wrong to assume that this box came from there. Context is everything you can't just assume it was a random distribution.
- In the context of it being a double yolk packing line the odds aren't 1 in 1000 they are 1 in 1, so of course the 4th and then 5th eggs were double yolks.
- Lesson : don't take things at face value and beware extrapolating hypothetical to real life : “Too incredible to be true” .. means the context is not what it first seems .. in a mathematical context they have assumed a random sample but they were wrong to cos clearly in a double yolker packing line the chance is not random
(BTW I guess that day, they had a certain number of orders for double yolkers and when that was fulfilled the remaining eggs were just boxed as large to fulfill the orders for large)