What's the probability my second child will be a boy?

>>  Friday, March 09, 2012

Probability is my archnemisis, it intrigues me and yet regularly baffles me at the same time.

I mentioned it before in seriousness here and more light heartedly here.  

Anyhoo - back to the sex of a second child (if you though for one minute I was expecting LOL). The question being :

I have 2 children, one of which is a son what is the probability of both children being boys.

The clear answer to which is 1/3. Ok, if your not into logical thinking skip to the comments box and pat me on the head now.

A 1/3? I hear myself and you ask!  Yup.  But everytime I remember the answer is a third I have to walk through the cold hard steps of why.  Here we go:

There are 3 possible ways I could have 2 children where one is a boy:

boy, boy
boy, girl
girl, boy
girl, girl

So the chances of having 2 boys is 1/3 - see, simples.  So why do I have to think so hard about it every time?

The problem with probability is there is the gamblers fallacy (stick with me) that will make us start to talk about 'likelyhoods', that's bound to throw you off a path.

But hang on a moment if the gambers fallacy is coming into play here surely the answer is 1/2 regardless?  No, it's all about the way the question is worded and possible outcomes.

If I'd have said "I have 2 children the older of which is a son what is the probability of  both children being boys" then the possible answers are

boy, boy
boy, girl
girl, boy
girl, girl

So the chances of having 2 boys then is 1/2.

But this is about simple mathematics it ignores genetics (and twins!).

So why are you droning on about this I hear you ask?  3 reasons:

Because the news recently declared (yet again) that people aren't embarrassed to say they are bad at maths and should be.  I  disagree because 'good' is relative term.  I am happy to discuss probability but would declare I am bad at maths.  I probably mean I'm not as good as I would like to be and anyway my mental maths stinks but that's because it's a muscle, use it or lose it.

Because I've noticed recently that the more I blog about things I think are going to be really interesting to people the less comments I get, so I'm in reverse psychology mode.

Because I stumbled upon a set of short videos about critical thinking aimed at school children and they set me thinking and that's rarely good for you dear reader.  But they are worth a look:

Here is the Gamblers Fallacy:

and the full set from Bridge8 can be seen here

I promise I'll start blogging again about 'the crazy things those darn kids say' one day soon, do stick with me in the meantime!


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