# Your statistics lesson of the day

Despite staggeringly long odds of 11 billion to one – a wife recently cracked open an egg to find four yolks inside.

The odds of this happening are 1 in 1.

Because it has happened.

The odds of any one egg having 4 yolks may indeed be 11 billion to one.

Yes, of course, trivial and pendantic, but this sort of misunderstanding (sort of, not exactly) is what led to Sally Clark serving time.

## 24 thoughts on “Your statistics lesson of the day”

1. Indeed; and Sally Clark didn’t just serve time, she was only freed when other evidence was found—whether the judiciary understood what odds mean is very uncertain. And she didn’t just serve time, it broke her.

2. According to that famous website egginfo.co.uk 11.8bn eggs are consumed in the UK each year so it seems we would expect one of those eggs each year to be like that. To be fair the article does state that it’s likely to be the only one this year. The bigger question really is why is this newsworthy?

3. “The bigger question really is why is this newsworthy?”
Can remember hearing the answer to that one in the Cheshire Cheese pub, in about 1967.
“Coz it’s August, mate.”

4. It didn’t just break her – it killed her.

5. My stats prof had this sensible advice: if you toss a coin and it comes up heads twelve times in a row, check to see if there isn’t something wrong with the coin.

6. eh? you’re not allowed to describe the ex-ante odds of anything that happened, because ex-poste the odds of everything happening is 1?

I do not see anything logically or grammatically wrong with writing: despite x being very unlikely, x happened.

7. “I do not see anything logically or grammatically wrong with writing: despite x being very unlikely, x happened.”

But (to be pendantic) that is not what was written. The Wail writer made an attempt at a mathematical statement, so it should be judged as such.

8. Well taking the quoted sentence alone the probability of “a wife” cracking open an egg with 4 yokes over an unspecified period of time is pretty much 1.

9. There’s an excellent YouTube video of a magician flipping a coin 10 times and it coming down heads all 10 times. The coin is perfectly ordinary, but he was filming for about four days before he managed to get 10 times in a row.

10. First time I played Baccarat I won 10 hands in a row, much the same as getting heads each time in a coin toss. I guess it happens to one in every (approx) 1024 first time Baccarat players.

11. The misuse of stats by authority should be a hanging offence, not just to avenge the sufferings of Sally Clark, but also in relation to the deaths of those too poor to keep warm, the benighting of developing economies by expensive fuel, the misuse of the taxes of productive people to subsidise the academic/political/fascists feasting off worbal gloaming…

12. Tim N / D John –

I (and the prof) wasn’t of course saying that it can’t happen. Just that if something very unlikely does occur, it’s worth considering why.

13. TMB I’d say that if you hear about it happening then meh… but if it happens to you then yes it’s worth checking out 🙂

14. The crime of the people who killed Sally Clarke was not ignorance (or disregard) of ex-poste probability but ignorance (or disregard) of conditional probability.
Whatever, they will all still burn in hell.

15. As some have pointed out, odds of 11 billion to one mean that for every eleven billion events, you EXPECT it to happen once. Long odds just mean something is expected to happen infrequently.

16. Any prosecutor using the prosecutors fallacy should be fired and never allowed near a court again. Are lawyers not trained in these things?

I think I also read about a nurse being convicted on stats alone because several patients died. Maybe in that book Bad Science which is quite good considering Goldacre is a raving leftie.

17. Once upon a time the roulette wheel in Monte Carlo came up black 26 times in a row.
The casino made a fortune because by the tenth time word had spread and everyone was betting on red until they ran out of money.
Each spin is independent, nothing to do with what happened last time.
But cot deaths are not independent, your chances of two or three are actually higher is one has already happened.

18. I could have fucked this up but I make it one in 67 million for a roulette spin to be the start of a 26 run of the same colour. 1 spin a minute is half a million spins a year so you’d belooking at it happening on each table about once every 50 of years. Given the number of roulette tables in the world you’d think it would happen somewhere quite often. However, should it happen to you should you think you saw a one in 67 million chance or have you been robbed? Depends on the number of dodgy wheels out there; Baysian stats and what not. I find this stuff quite interesting.

As BiF says each spin is an independent event but you try explaining that to the Chinese! I’ve had them laughing at me in Macau because I’ve bet on the ‘dealer’ at Bacarrat even though that hand has won the last few. idiots. (actually I’m the idiot for playing it in the first place but ho hum)

19. As any fule* kno, there is a difference between ‘probability’ and ‘likelihood’. To illustrate: 1) I roll a fair die 20 times. What is the probability that it comes up six every time? 2) I roll a die 20 times and it comes up six every time. What is the likelihood that it is a fair die? Colloquially, likelihood and probability are used interchangeably, but they describe different things. This takes on particular significance in the context of Bayesian inferential statistics.

* fule who has studied stats beyond the noddy level, that is

20. We are somehow absolutely rubbish at statistics.

Out of the following tosses of a fair coin, which is most probable:
HHHHH
TTTTTT
THHTH

nearly everyone would choose the third sequence, but it’s no more or less likely than the others.

I’m suspicious about the use of stats in criminal trials. Few lawyers, and even fewer judges, can do even basic math.

Take the example of DNA testing. Only a one in million chance that this crime was done by someone else.

My reaction would be to ask of the other 59 suspects had been investigated and cleared. Most juries would be swayed by the big number.

As Barbie say, Math Is Hard. But it ain’t that hard if even I can get a grip on it.

21. @ bif
Trick question: if you ask which is the most likely: six heads, six tails or three of each, the answer is the last and most people misunderstand and they think thjat you are asdking*that* question. So it is not a failure of their ability to do simple maths – it is failure of their ability to identify what the question is.

I agree with the rest – some judges are not just unable to understand maths – they flatly refuse to do so. A few years ago one provoked outrage when he ruled that actuarial evidence could not be accepted.

22. @ TMB
And before tossing heads and tails, check that there is a head on one side!

23. @ JeremyT
One of their crimes was describing someone who did not understand what he was talking about as an “expert witness” whose advice the Jury should follow.
It wasn’t the Jury’s fault – they reached a verdict based on what they were told. They are not allowed to consider stuff outside what they have heard in court. The last time I served on a jury, I felt that what someone could see from where was relevant so I drove over to near the scene of the crime and went for a jog* (middle-aged joggers are the modern equivalent of the cabby in “A Study in Scarlet” – invisible): I was politely** but soundly reprimanded by the Chairman of the Jury – only if a juror had enough expertise in both statistics and medical science could he/she have challenged the “expert” and only by asking the judge permission to ask a question through him.
*difficult for someone who used to run, but needs must …
**probably he was a schoolfriend of my elder son – I hadn’t recognised him

24. Sorry, but i think this accusation is completely unfair. What the Mail writer says does not suggest that he was talking about the odds of this happening in general. It’s perfectly clear from the context that he was referring to the odds of any particular egg having four yolks.