172. What are the Chances?

In 2012, the Royal Statistical Society asked 97 MPs a question on the maths of probability.  I don’t know why but possibly it was in the hope that many of them would get it wrong and then we could all scoff and say that the average MP is rather dim.

I am not a mathematician but I suspect that the simplest question of all on probability would be something like, 

“If you spin a coin, what is the probability of getting heads?”

The answer is that there are two equally possible outcomes when a coin is spun; one is heads and the other is tails and so the answer is that the probability of getting heads is ‘one in two’ or, as mathematicians would say, ‘0.5’.

I would say the answer is ‘one in two’.  Surely, ‘one in two’ is a notion that is simpler to understand, than ‘0.5’?  Maybe, this is one reason why so many people are very happy to say, “Maths?  I’m useless at maths.”  

In a piece I posted here in 2013, I wrote that Gwyneth Paltrow, Mariella Frostrup and Ruby Wax all seemed to be quite proud of being “useless at maths”, whereas no one ever says they are useless at English.

Before MPs were asked the probability question, three quarters had said that they felt confident dealing with numbers.  I suppose that means that they felt they were reasonably good at maths and certainly not “useless”.

The question they were asked was, 

“If you spin two coins, what is the probability of them both being heads?”

Despite their apparent confidence, 47% of the Conservative MPs and 77% of Labour MPs  got it wrong.  Are Labour MPs dimmer than Tories?

That thought is not for me to comment upon, although I will say that David Lammy’s performance on the television quiz, Mastermind, makes me wonder.  

He answered “Antoinette” when asked for the married name of the scientist, Marie, who discovered radium.  Then, he told the question master that Henry the eighth was succeeded by Henry the seventh.

The answer to the question that was asked of the MPs is 0.25 or as I prefer to think of it, one in four, as only one of the four equally likely outcomes is two heads.

I had a haircut in the beginning of October which, because of Lockdown, was the first one since February.  

I had been told about Lena, a woman who has gone to extraordinary lengths to ensure that both she and her clients stay safe from the threat of Covid.  

Her business is 16 miles away but as it was a choice between having my hair cut by either her or Caroline, I chose the relaxing drive to Bedford.

Caroline did cut my hair once when I was bedridden for several weeks in Cayman and she would be the first to admit that she made a quite dreadful job of it.  After it was over, she stood back, surveyed the scene of the carnage she had created and then, by way of both explanation and perhaps an apology, said to me,

“You know, cutting hair is a lot like playing golf.  They are both more difficult than they look.”

Lena is from Romania and as she cut my hair, she talked incessantly.  I mean, she never stopped!  

Like many (most?) people, I hate the tedious, mundane inconsequentialities of the strained haircut-conversation.  I want silence throughout it all and so, whenever a response from me was expected, I either grunted, “Yes” or “No”.

We were ten minutes in when, inevitably, Lena asked what my job had been before I retired.  

“Teacher.” I mumbled.

“So, you went to university.  Which one?”

“Durham.”

“My son is at Cambridge. What ages did you teach?”

“Eleven to eighteen,” I mumbled.

“Ah, to A’ level.  Is that right?”

“Yes.”

“What subject?”

I knew this was coming and so I was ready to tell a lie:

“Maths.”

From past experience, that would shut her up.  When I said I had taught maths, it should have brought the “I am useless at maths” response and conversation would abruptly stop.  It always works at a barber’s or hairdresser’s.

Not this time, it didn’t. 

“Oh, really?  What’s your favourite formula?”

My what?  My favourite what?  What the hell!  I didn’t know formulas had names or people had feelings about them.

“I haven’t got one,” I mumbled.  “They all have a purpose.”

“Well, yes, of course they do but mine is Oilers.”

“Yes, I find that’s a handy one when my car needs a service,” I said, hoping that was a stupid enough response to be amusing.

It clearly wasn’t because Lena just carried on talking about irrational numbers and other things that I didn’t understand at all.  I sat in silence, grunting affirmatively and nodding wisely every now and then.

I tried to change the subject from maths to anything else but I couldn’t because Lena had found someone whom she thought to be a kindred spirit and she wanted to talk maths.

Eventually, she did stop talking about maths and then I heard about her life in Romania where she had been an actuarial analyst (???).   When she arrived in England 13 years ago, her English had been very poor and she had taken up her hobby of hairdressing.  Now, her English is perfect and I think she cuts hair fairly well too.

As soon as I got home, I asked Caroline (who really is a mathematician) to tell me about Oilers formula.  She was very surprised to be asked but told me that it was a formula devised by Leonard Euler (pronounced “oiler”) a Swiss mathematician and it was one of her favourites too. 

She tried to explain it to me but despite its apparent “beauty”, I lost track after about thirty seconds which was at about the same time I lost interest as well and I told her so.

Undeterred, she attempted to revive my interest in formulae by describing the intrinsic and inherent elegance of the formula for the surface area of a sphere but again, she failed.  I am certainly no mathematician.  

Now, I have a problem.  The next time I need a haircut, do I go back to Lena and run the risk of being exposed as the fraud that I am or, do I let Caroline loose on my hair again?