OT BBC 'Maths' Quiz

Although quite good at maths, I'm disappointingly crap at stats. I
really don't see how knowing the sex of one of the kids affects the
outcome of the ther child - surely it's still 50/50?

 

<boggle>

 

Oh bugger, and there was me thinking i'd got one over on the BBC!

Thanks for setting me (and the wife) staight.

 

Take 100 families with two children. On average 25 will have two boys,
25 two girls and 50 one of each (i.e 25 boy/girl and 25 girl/boy).

The family next door isn't one of the first 25 (two boys) so it is one
of the last 75. Take one girl out of each and you have 50 families
left with a boy and 25 left with a girl - so 1/3 with a girl.

 

I guess the only thing I see wrong with this, is the original question
didn't specify that the two kids were from the same family. I suppose
that isn't supposed to matter, but my beer-addled brain isn't quite
able to figure out how the odds of the 2nd child being a girl isn't
50/50 if there is no relationship between the two children.

 

ah, ok, that's my first mistake - I didn't assume that the kids were
from the same family, tho I'm not sure this affects the result.

Surely that's 24/49? (Tho obviously tends to the same answer).

<screws up eyebrows> So, what's going on here - we're using the
distribution of boys and girls in the whole population (50/50) to
infer something about a sub population derived from the main
population?

 

They don't have to be. Next time I explain it I'll not make that
supposition - I'll start "take 100 pairs of children"!

You'll just have to ponder it a bit further! The following may or may
not help you.

If you knew either that the unseen child was older than the visible
girl, or that the unseen child was younger than the visible girl, then
the probabilty of the unseen child being a boy or girl would indeed be
50/50 - because you would have ruled out another 25 of your starting
families (or pairs of children!).

 

It doesn't.

I meant remove a girl out of each of the 75 families, to leave one
child in each of the 75 families.

In one sense, yes. I was explaining in terms of actual numbers
something that is correctly explained only in terms of probabilities.
Probabilities tend not to depend on sample size, whereas actual
results do.

 

Mike Cook wrote

Well that is bollox cos I feel just fine thank you very much.

 

Yeah, I got 11/15, but I'd already read the answer to the disputed question
here and wouldn't have gone for 50% anyway, so I guess it's an 'adjusted'
10/15.

However, I agree that a lot of them are lucky guesses ... the rice & chess
board on, for example. I can work out what 2^64 is, but I have literally no
idea how many grains of rice there are in the world, so it doesn't help my
answer at all.


--
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The speccy Geordie twat.

 

At present I’m siffed as a part but is there a factorial involved?
good night

--
Bob
Currently borrowing a black and red Yamaha XJ750 with fuel injection
Present: Honda XL125RF (FS)
Past: Honda CG125
bob at homeurl tomato dot co dot uk
remove the red fruit if you’d like to email me.

 

No, because the question is, "Would there be enough rice in the world to
fill that last square?"[1], not, "Would there be enough rice in the world to
fill all of the squares?"

Although it would have to be pretty impressive chess set to be able to fit
2^64 grains of rice on, irrespective of the availability of rice.


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AndrewR, D.Bot (Celeritas)
Kawasaki ZX-6R J1
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BotToS#5,SBS#25,IbW#34, TEAR#3 (and KotL), DS#5, Keeper of the TFSTR#
The speccy Geordie twat.

 

Yes, yes, I've heard the question before ... my point was there _might_ be
18,446,700,000,000,000,000 grains of rice in the world ... I don't know.

How many grains in a tonne of rice? How many tonnes produced, annually,
world-wide? Can I be arsed to Google to find out?

No, I can't.


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The speccy Geordie twat.

 

I suspect that's why they specified politicians and economists; as they tend
to work in American billions.


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The speccy Geordie twat.

 

Charles Dodgeson was a mathematician.

Tenuous, I know.

 

You can blame politicians for the confusion, in 1974 (when I was born)
Harold Wilson announced to the House of Commons that the meaning of
"billion" in papers concerning Government statistics would be 10^9, in
conformity with U.S. usage.

Isn't the internet brilliant..


I also found this useful look-up that shows just how far out of step
american numbering is with 'proper' english numbering.

U.S. Traditional British
10^6 million million
10^9 billion thousand million or milliard
10^12 trillion billion
10^15 quadrillion thousand billion
10^18 quintillion trillion
10^21 sextillion thousand trillion
10^24 septillion quadrillion
10^27 octillion thousand quadrillion
10^30 nonillion quintillion
10^33 decillion thousand quintillion
10^36 undecillion sextillion
10^39 duodecillion thousand sextillion
10^42 tredecillion septillion
10^45 quattuordecillion thousand septillion
10^48 quindecillion octillion
10^51 sexdecillion thousand octillion
10^54 septendecillion nonillion
10^57 octodecillion thousand nonillion
10^60 novemdecillion decillion
10^63 vigintillion thousand decillion
10^303 centillion
10^600 centillion

Now, I wonder if I should correct our sales people next time they talk
about billion pound deals..

 

But you are no longer sampling from a population of families who have
tow children. You are sampling from a population of families who have
two children one of whom, is already known to be a girl.

If you disregard any genetic bias that may exist for particular
families to tend to have more boys than girls or vica verca, and
assume that the gender of each child is statistically independent then
the answer to your original question is 50%.

It is only if you do not yet know the gender of the first child can
you play with then numbers the way you have. Google for Bayes and
become enlightened.

 

As far as UK political and economic usage (as specificied in the
question) is concerned, a billion is 10 ^ 9. Scientists haven't used
names for numbers for decades, so there's not much point clinging to
the 10 ^ 12 version, unless you get some pleasure from moaning about
changing usage.

 

I've already said my explanation is flawed because I'm trying to
explain probabilities by using samples. This inherently wrong. If you
want sound reasoning then I suggest you apply Bayes theorem and you'll
come up with the right answer - if you do it correctly!

Nope - 33%.

I suggest you follow your own advice.

<thumbs through a few statistical books>

Alternatively, this problem, together with similar ones, is dealt with
entertainingly by Ian Stewart, Professor of Mathematics at Warwick
University, in his book "The Magical Maze". FWIW, He comes up with
33%.

 

As did mine.

That's not what I said. I said that science and technology doesn't
deal in named numbers, and hasn't done for decades. My understanding
is that the only time someone like Will or Ivan will use words like
million and billion is when they're talking to a layman.

<waits for one of the learned doctors to turn up and prove him wrong>