h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: The Boy or Girl Paradox - A18816663
Author: Alex 'Tufty' Ashman [!] - U566116


I'm going through a bit of a dry patch in terms of ideas for Entries at the moment, so here's something to fill the gap for the time being.

Alex

Interesting one.
It took me a few moments to suss out the questions. Perhaps a change at the start? Something like this perhaps?
----
Let's assume the ratios are ... Now:

On the one hand (case a)

On the other hand (case b)

The question is...
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Another read through later.

I was able to follow your logic until:


>>have either an older sister, a younger sister or a brother, thus making three alternatives.<<

and then you lost me.

Or twins!

OOps

I liked it! And yes, I did guess wrong initially, but then worked it out for myself before I read on.

TRiG.

Traveller in Time reading and reading again
"I admit you nearly had me on the wrong idea in the first paragraph.

However I do completely not follow the last:

>a paradox simply because the solution is quite counter-intuitive.

Does not make sense at all. A paradox is not putting the reader on the wrong track, a paradox is a logical equation reversing the True False outcome everytime you evaluate it.

I do find a logical equation here but it does not flip from true to false anywhere. Paradoxes have nothing to do with intuition, they can be evaluated with pure logic. "

I think you were right once, but as often happens, the English language has evolved, and "paradox" is quite widely used to describe this type of problem in probability theory. Mathworld describes "paradox" as "A statement which appears self-contradictory or contrary to expectations...", and the second alternative certainly applies here. (ref http://mathworld.wolfram.com/Paradox.html )

Alex, I'd like to see this in the guide, but I found it just a little dry. The Monty Hall problem is far easier to apply to an everyday situation, as we've seen quiz shows that operate it. Is there a practical example of this problem?

Icy

... And I agree with Lil - you should mention what happens with twins!

I've rewritten it a bit - I think I've made tha changes I was meant to


>>Is there a practical example of this problem?<<

"Every moment dies a man, Every moment 1 1/16 is born."*

Is that not a practical application?


*('Strictly speaking,' Babbage added, 'the actual figure is so long I cannot get it into a line, but I believe the figure 1 1/16 will be sufficiently accurate for poetry.')

Sorry, you lost me with that. You do talk Babbage sometimes.

It's no big deal, it's just that it would elevate it from being a mathematical exercise to being an everyday problem, and it would become more widely appreciated. Of course, if there isn't a practical application, then so be it.

Icy

I meant that the practical application is that families with boys and girls actually exist and are born all the time, but I suppose that's no more interesting than picking coloured buttons out of two bags

Yes, we have boys and girls, but at what point is it practically important to us to know that if a two-child family has one boy, then the probability of the other being a girl is two-thirds?

Could you extend the argument to a gambling scenario, for example?

How should I do that? To be honest, I find the idea that this problem might be used to trick people into parting with money a little odd.

Well, the Monty Hall problem is all about financial risk.

Ignore the boys and girls completely, and consider the premise that you have two items, each being one of two types. You know that one is type A, what is the chance that the other is type B? Does this risk scenario apply in a practical situation? It doesn't have to be financial of course.

*giggles*


It's like the odd socks in a bag scenario. How many socks will you need to pull out to make a pair?

Sorry, I will go back to my corner

Yes, but only if you have two bags, one with the left socks and one with the right socks.

How can you tell the difference

I've only one bag, but she normally folds the socks together in pairs.