A woman has two children, at least one of which is a boy...

[Provost Harrison]

To me, it looks completely different...I understand where you are coming from but surely you can reach it like this as well...

A woman has two children, at least one of which is a boy...

The probability that the other child also is a boy is thus 1/3.

Is this correct or incorrect?

A dissection: We know that one of the children at least is a boy, yes?

Look at the middle statement and the language, stating the probability that the other child also is a boy which indicates that the first child is a boy. Therefore the first criterion that at least one child is a boy is fulfilled. Therefore the gender of the second child is undetermined and unrelated to the gender of the first child. Therefore the gender of the second child is independent of the first child. That is the way I reason it.

[Jon Miller]

Originally posted by Provost Harrison
To me, it looks completely different...I understand where you are coming from but surely you can reach it like this as well...



A dissection: We know that one of the children at least is a boy, yes?

Look at the middle statement and the language, stating the probability that the other child also is a boy which indicates that the first child is a boy. Therefore the first criterion that at least one child is a boy is fulfilled. Therefore the gender of the second child is undetermined and unrelated to the gender of the first child. Therefore the gender of the second child is independent of the first child. That is the way I reason it.

It says other child

not second child

there for the other is refering to at least one child is aboy

Krazy is still right

Jon Miller

[Rex Little]

To those who still don't believe Krazy and Jon, I propose a wager. We'll survey 100 women who have exactly two children, including at least one boy. (Shouldn't be hard to set that up in an online chat room or something.) If at least 51 of them have a girl in addition to the boy, you pay me $1000. If not--if at least 50 of them have two boys--I'll pay you $1500. If Harrison is right and I'm wrong, I'm offering you 3/2 odds on a 50-50 bet. Any takers?

[Provost Harrison]

Let's make that monopoly money, and you can do the donkey work

[devilmunchkin]

krazyhorse: why don't you educate me rather than just telling me i'm stupid.

i still don't see how i could be wrong since the father is someone who determine's the sex of the child. Fraternal twins will be of the same sex because they are fertilized by one sperm..so that would help if that info was given.
otherwise, it really does depend of the amoung of sperm that man has in that one ejaculation containing sperm with X chromosones and those with Y chromosomes. THe number will vary dending on how many times in a single..umm...tryst that he's ejaculated into her (it changes the number of sperm inside her) and also it depends on how many are able to get part her natural sperm barriers (sperm enter into an acidic environment which most don't get past). You have to go further in the comlpexity of the numbers because the fertility of each man is different...he might be shooting some weak ones or he might be a loaded elephant gun.
it all depends....and no...you're right..i can't attach numbers to it.

[shade]

Re: A woman has two children, at least one of which is a boy...

Originally posted by Boddington's
The probability that the other child also is a boy is thus 1/3.

Is this correct or incorrect?

This is absolutely correct:

If a woman has 2 children the possibilities are

[B,G],[G,B][B,B][G,G]
(always order from young to old=> that's why the first two are different)
==>If there is at least one boy there are 3 possibiliyies left
[B,G],[G,B],[B,B]
-->Only 1 in 3 has 2 boys so chance is 1/3

Shade

[Jon Miller]

Originally posted by devilmunchkin
krazyhorse: why don't you educate me rather than just telling me i'm stupid.

i still don't see how i could be wrong since the father is someone who determine's the sex of the child. Fraternal twins will be of the same sex because they are fertilized by one sperm..so that would help if that info was given.
otherwise, it really does depend of the amoung of sperm that man has in that one ejaculation containing sperm with X chromosones and those with Y chromosomes. THe number will vary dending on how many times in a single..umm...tryst that he's ejaculated into her (it changes the number of sperm inside her) and also it depends on how many are able to get part her natural sperm barriers (sperm enter into an acidic environment which most don't get past). You have to go further in the comlpexity of the numbers because the fertility of each man is different...he might be shooting some weak ones or he might be a loaded elephant gun.
it all depends....and no...you're right..i can't attach numbers to it.

It is not biology, it is probability

if the biology is messing you up, take it out

instead imagine two coin flips

now if at least one is heads, the probability of the other being heads is 1/3

since the possibilities are
1 h, h
2 h, t
3 t, h
4 t, t

notice that number 4 has no heads result, so we can throw it out

that leaves 1, 2, and 3

of the three remaining, (that have at least 1 heads) how many have another heads

since that is one the probability in the question is 1/3

now replace two coin flips with two children
and heads with boy

better?

Jon Miller

[Imran Siddiqui]

To add on (for dm)...

Say the probability of having a boy is 50%. The first child is a boy. Therefore the odds of the 2nd child being a boy should be less because it eventually should end up at approximatly 50% .

[Jon Miller]

no

that is the poiny

a child is a boy

not the first one

Jon Miller

[Chowlett]

And Imran's assumption is false anyway. It would imply that a coin that has been tossed 10 times and come up heads each time (roughly 1 in every 1024 trials) would be very much more likely to come up tails next time than a freshly minted one - which is ludicrous. In both cases, the second "happening" is independent of the first "happening".

[Urban Ranger]

Re: Re: Re: A woman has two children, at least one of which is a boy...

Originally posted by KrazyHorse
1st: The woman has two children. Therefore there are 4 distinct possibilities

1) eldest: boy, youngest: boy
2) eldest: boy, youngest: girl
3) eldest: girl, youngest: boy
4) eldest: girl, youngest: girl

2nd: At least one of the children is a boy. Therefore possibility 4 is eliminated. There are 3 distinct possibilities, each of equal magnitude. 2 of these involve her having one boy and one girl. One involves her having 2 boys.

That's wrong because you are distinguishing case 2 and 3.

For the question, these two cases are exactly the same. It doesn't matter if the oldest or the youngest is the boy.

There are 3 cases:

1. 2 boys
2. 1 boy and 1 girl
3. 2 girls

Having a boy eliminates situation 3, so the probability of the other child is also a boy is 50%.

[Dauphin]

UR there is no degeneracy. Both of the "One boy, one girl" cases have to be counted seperately.

[Chowlett]

Originally posted by Sagacious Dolphin
UR there is no degeneracy. Both of the "One boy, one girl" cases have to be counted seperately.

Since they are equally likely, and exactly as likely as boy-boy or girl-girl. If you poll a set of families with 2 children, you will find twice as many with boy-girl as you will with boy-boy.

[rah]

This is amusing.

The difference is when you make the prediction. Before or after the births. Before the births it is approx 50% on any given birth. After two births, it's 1/3. As nicely shown by many posters.

Same thing with coin flips. If after 7 heads, whats the odds of the next flip being heads. 50%. But if you ask what the odds of 8 heads before any are flipped, then considerably higher

RAH
So much for making it clearer.

[Rogan Josh]

Is it just me or is all this bloody obvious? (Clearly not - since there is so much debate....)