No but it comes with a crown race…

aaaaggghhhhh, FFS!

OK, how long is "all day"
how long does he camp for ?
How long does it take him to walk down ?

(trick questions?):
same route down ?
what do you mean by position ?

(seems I dont do maths or logic) :

so if IGM can make that 50% argument for the eldest I think I can make it for the youngest, too

If so, it doesn't matter which the 1st mentioned kid is, the answer is 50%
So why isn't it 50% anyway ?

ok four outcomes M M , M F, F M , F F
with one being female we get M M , M F and F M so 1 in 3 of two males
If we know the eldest is male we have only M M and F M as options so 50/50 of two males
We reduce the number of combinations so change the odds.

24 hours assuming lots of things that just wont happen in the real world yes but not really as thye will be facing another direction unless they walk backwards

I'm sure there's some hormonal thing that ups the chances of the second being a girl if the first is.
Stat that 😛

well, yeah junkyard

but if you tell me that one of your kids is male and I say "If he's the eldest, there's a 50% chance you have 2 boys and if he's the youngest, thers a 50% chance you have 2 boys" how am I wrong ?
(I need something verbal to back up the maths because I'm just not feeling it for 1/3)

You're not wrong.

But if I don't tell you he's the oldest or youngest the odds are 33%.

Right about now you will be saying how can they be anything other than the oldest or youngest – but the knowledge about the family makes a difference to what you can say about them.

but if you tell me that one of your [two] kids is male
and I say "If he's the eldest, there's a 50%
chance you have 2 boys and if he's the
youngest, thers a 50% chance you have 2
boys" how am I wrong ?

You're not. You'd be correct.

Is the answer baby robin?

Sorry folks, I had planned on responding prior to this, but seeing as I got dragged away from t'internerd I couldn't get back on..

GrahamS, to answer your question, I am not sure as I wasn't the original one to ask the question, I heard it on Radio 4's More or Less, but it looks like it's made it into the New Scientist as well… it was originally asked at a maths/puzzle convference in the US.

However, I would guess that the Tuesday only relates to a the known boy.

Looking through the answer myself, I can see how the maths works out. Essentially the extra information you now have means that the order of a B B family is important with BTu B being different to B BTu unlike in the original where B B was just a single result.

Unlike Junkyard however, I think that this result is followed in the real world and would be backed up empirically. You should be able to reproduce this in a spreadsheet in just the same way as GrahamS did for the original.

As for the 50%ers… hehehe… now, I have these three doors, behind one of them is a stack of cash… ;o)

Unlike Junkyard however, I think that this result is followed in the real world and would be backed up empirically.

I dont agree but the reason the probabilities change is because we are only sampling a percentage of the TOTAL possible outcomes and the odss within that subset are as stated the actual odds have not altered.
MM MF FM FF
is reduced to MM MF FM hence the 1 in 3 as we ignore 25% of reality. I suspect the Tuesday does the same However I cannot really see how the dat affects anything in this example. In the first example the child must be born on a day being told which day it is has not altered anything in the real world. I agree them aths /spreadsheet will hold but it is not "real". It will not be observed by actually monitoring of reall births IMHO.

I agree them aths /spreadsheet will hold but it is not "real"

What if you used the spreadsheet to count a "real" collection of say 10,000 people that actually met the criteria? Would it become real then? 🙂

It will not be observed by actually monitoring of real births

As pointed out, real births are no where near this simple. The problem is set in a statistically perfect world, where every birth has a 50:50 chance of being either one boy or one girl and there are no troublesome factors like genetic predispositions, environmental influence, multiple births, IVF, XXY "girlboys", etc etc

At best you might see a rough approximation of this in the real world.

But yes, I'm reasonably convinced that if you monitored births within this imaginary construct then you would see the figures discussed.

What if you used the spreadsheet to count a "real" collection of say 10,000 people that actually met the criteria? Would it become real then?

That is my point it would be real but would come out as 33% not 13/27.
Yes my assumptions are made in a statistically perfect world as well.
Essentially you are arguing that the day your child is born on affects the likelyhood of their gender and i say that is B0ll0cks for. The gender of the sibling alters the likelyhood of their gender I cannot see how day of birth does this as all children are born on a day] and i has has no bearing on likelyhood of gender.
I am astarting to get paranoid that I am doing a Smee here though 😉
I need to do asomemaths n this have we just reduced the set of all possibilities even further so that we have 13/27 but for less than 75% of the total births?

I understand your confusion Junkyard, and share it slightly.

I think the key is that "The gender of the sibling alters the likelyhood of their gender" isn't really true. It just alters the likelihood that we are dealing with a child in a particular sub-group.

So the same applies to adding the day of the week information. It doesn't really mean that "you are arguing that the day your child is born on affects the likelyhood of their gender " it just means the sub-groups we must consider have changed and so have the probabilities that you are dealing with a child in a given sub-group.

I think.

If I get time I might do a spreadsheet…

yes get the first bit we have removed one of the four posiibilitie shence 1 in 3 with you re sub set.
I agree with the next bit as well re the maths but I cannot believe thtat day of the week actually alters the probability of the gender after all in the first one the baby was born on a day of the week just because we now know which one I cannot see hwy th eprobabilities order.
I suspect the maths is correct but I dont agree with the conclusion reached that is that the odds have changed – your spreadsheet will show it as you describe no need to do this for me but if the inner Geek feels the need dont let me stop you 😆

My Inner Geek is strong:

http://spreadsheets.google.com/ccc?key=0Ai9dvO8nev8icF9INW8yU2VwM1BOeFBoQjFDamItRGc&hl=en_GB

The spreadsheet shows 1,000 pairs of siblings. It is 50:50 whether each is boy or girl and 1 in 7 for the day of the week they were born.

It should re-randomise them every time you refresh it.

I'm currently seeing: 119 pairs where at least one child was a Boy born on a Tuesday and of that 54 (45.9%) had a brother. 😀

Obviously it would be more accurate with a larger sample size, but I think it demonstrates the point 🙂

bows down at the alter of stats but you have linked to the old boy /girl one not the new one…unless i am as bad at computing as I am at getting this.

bows down at the alter of stats but you have linked to the old boy /girl one not the new one…unless i am as bad at computing as I am at getting this.

Try Sheet Two (tab at the bottom of the spreadsheet)

(did it work? did you see?)

sticks head in sand and refuses to play !
Yes and I dont fault the maths but I dont understand what has been removed to increase the odds. With the first example we loose FF hence the change what is it in the second that has been removed by knowing birth day? Will have a proper look / think tomorrow and you can help lead me to the light 8)

graham, can you easily add a cell or two to count how many (or, rather %) boys have:

older or younger brother
older or younger sister

❓

Yep, I'll do it tomorrow. But is should be around 50% for both.

Done, as expected:

Boys with brothers ~ 25%
Boys with sisters ~ 50%
All girls ~ 25%

Pretty much as per the original problem. 🙂

But is should be around 50% for both

as expected (25%, 50%)

😯

Yeah, yeah, I misread your query yesterday. 😀

Anyway, does that help?

(no 🙁 ) cheers

Lol, oh well I tried. At least it demonstrates the maths is "real world"

scaredypants… try looking at it like this…

If you assume he is the eldest then there is a 50% chance the younger child is a boy

If you assume he is the youngest then there is a 50% chance the older child is a boy

That gives an overall 25% chance that the both children will be boys, which agrees with GrahamS's spreadsheets above, but this is the chance for 2 boys in the population as a whole.

By then using the knowledge that the family has to have at least one boy, that means that we can ignore all those families with 2 girls, which is 25%.

If we take the whole sample to be 100 families, this means that the number of families with 2 boys is 25/(100-25) = 1/3 or 33%.

Any better?

Funkynick – I'm way beyond help

I can "see" the statistical answer but I can't get it to agree with my own special logic*

*which would say that what you said about probabilty above should, if correct, also apply to him having an older or younger sister – which would leave us with a 33% chance of his sibling being neither a girl nor a boy 😐

Junkyard… you are not losing anything to increase the odds, nor is the day of the week having any effect on the likelihood of a child being born one sex or another… it's simply a matter of probability.

What happens is this…

In the previous problem, where we just know that one child is a boy, which gives the answer of 33%, we only know the following:

There are 2 children
One is a boy
The birth rate is an idealised 50:50 split

This means it only allows us to have four choices of how the family is made up:

GG BG GB BB

And so losing the GG option as we know there is at least one boy, gives us the 33% answer.

However, in the new problem, where we also know the boy was born on a Tuesday, this gives us extra information and so an extra option… so that now we have the following possibly options:

GG BTuG GBTu BTuB BBTu

Once again losing the GG option leaves us with the remaining 4, and the maths continues as posted on the first page, giving us the answer of 13/27.

So, by being given the additional information it means that the order of the birth for the two boys options becomes important, whereas previously, the order for the two boys was unimportant as all we knew was that there was at least one boy.

All this means is that as we get more and more information about the children involved, then the closer and closer the answer gets to being the 50% that a lot of people thought was the answer to the original question.

Any clearer?

scaredypants… thinking about it a little more, I have a feeling that this is one of those areas where I am not sure we can actually make those assumptions like that and then combine them unless both children are boys.

Stick with me here…

Due to the assumptions, firstly that there is an older boy in the first one, and that there is a younger boy in the second, these can only both be true if both children are boys, and that was how we got the 25% above, by multiplying the two 50% chances, so giving the chance that both those situations were true.

If we try it with older boy and younger girl and then younger boy and older girl, combining those would give trouble as both can't be true at once, so the chances of both happening at once is zero, so if one is true, then the other is not, and vice versa.

So, to get the answer for the probability of having a boy and a girl, you would subtract the probability of getting 2 boys from 100 to give the answer… 66%

I think…

This might be way out as I may be stretching my knowledge of probability just a tad here!