Dot writes: I’ve just bought and started a book by Jeffrey S. Rosenthal, *Struck by Lightning: The Curious World of Probabilities*. I was drawn to the topic for a general reason and a specific reason. The general reason is that I think probabilities are bandied about recklessly in the press by people who don’t understand statistics trying to persuade or terrify other people who don’t understand statistics. A made-up but verisimilar example: ‘if you send your child to nursery school s/he has a 20% increased risk of going to Superquinn and shooting everyone’. You recognise the kind of guff. The specific reason is to do with contraception. I was told that the diaphragm (a rather rare method these days) has ‘a pretty decent failure rate’, which my doctor quoted as ‘about 20%’. What on earth does that mean? A normally fertile couple having regular sex only has about a 20% chance of conception in each cycle when not using any contraception at all. (There I go with another statement of probability – but at least that one is a little easier to understand!) If the 20% figure means 20% of women using the method will get pregnant, does that include women using it incorrectly? Over how long a period of time? Or does failure mean sperm getting through, even if they don’t then strike the jackpot? I don’t expect Rosenthal to clear up that particular puzzle, but it was my rather unhelpful consultation on this topic that particularly focused my mind on how such figures are summoned up to influence one’s decision-making, and how little one really learns from them.

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Probabilities (being used in this way or any for that matter) are highly dangerous because they seem simple to apply but in fact it is a area of mathematics that is quite tricky and often very badly misunderstood – and I speak from the standpoint of one with a maths degree who has suffered this area greatly.

The example of 20% failure rate given as it is is very misleading as the usual changes of conception for a couple with no problems who are actively trying to get pregnant, so trying more than once in a cycle to get the timing right is quoted as being around 12-12.5% about a 1 in 8 chance.

The 20% failure rate of the diaphragm needs to be applied to this rate of success. So for a couple who are at it like rabbits but using a method of conception that can fail one time in 5 you are looking at a conception rate of around 1 in 40 (1/8 * 1/5)

A couple who have unknown fertility issues with no chance of getting pregnant would find that for them the rate of failure of the diaphragm is 0%.

Of course this begs the question of how this 20% rate came about…

But since this is an area of maths that is so badly taught in schools, especially when you are looking at compound probabilities which is where they really come into play, it quickly gets dropped in favour of doing the Calculus option of the paper instead (I know I did and only really did probability and dreaded stats because it was a key component of looking at systems testing).

This is also because the logic required in thinking out these problems isn’t taught in schools; and now I sound like Professor Kirke – what do they teach them in these schools? 😉

I apologise for a comment that was longer than the original post 😉

Thankyou for a comment that was considerably more informative than the original post!

I confess I’m not sure where I read the 1 in 5 figure for a ‘normal’ couple’s chance of conception in each cycle. Just now I was waiting in the pharmacy for a prescription for Hugh (who has an interesting blotchy rash), so I had a look at the British Medical Association booklet on infertility. They say that the chance of conception in each cycle for a normal couple ranges from 1 in 3 to 1 in 20, with 1 in 6 about average. That has a convincing ring for me because it recognises that it’s normal for people to vary. (It doesn’t say what kind of average that is.)

The main problem with trying to come up with probabilities for things like chances of conception is that there is a wide range of variables which may or may not come into play for any given couple; and combination of said variables. Its definitely no coin toss 😉

Hope the little one is feeling better soon. I’m currently going completely nuts -I just want this kid out of me now! I can barely walk from the living room to the kitchen without feeling like I am carrying around a very knobbly bowling ball.

One thing that puzzles me about probabilities is when and how to update probabilities in light of what you know. It someone chooses a random card from a deck, I know there’s a 1 in 4 chance it’s a heart. If they tell me it’s red, I know it’s now a 1 in 2 chance. But what do I do about a case like the 2004 US election. In the past, no challenger has beaten an encumbent in an election held during a war (or so I heard). But in the past, the taller candidate has always won (or so I heard). Kerry was the challenger but taller than Bush. How should I update my prediction in light of the new information?

I think for something like elections which are based a lot on perception rather than actual measurable outcomes and/or decently sized samples as in the deck of cards instance, there doesn’t seem to the data on which to base a decent probability – also hampered by the way the electoral process works in the US, as it isn’t necessarily based on the number of popular votes.

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