Puzzle: I have two children ...

[Santino]

It helps to understand this if you imagine putting the boy behind door 1, and then the other child behind door 2 or door 3, with the other door having a goat behind it.

This is on ITV from next Saturday, presented by Ant and Dec.

 

[ymu]

You know that one child can't be a girl so how can you have both GB and BG?

We know that there can't be two girls - BG and GB are both consistent with the information that at least one child is a boy, as is BB (but not GG).

 

[bi0boy]

We know that there can't be two girls - BG and GB are both consistent with the information that at least one child is a boy, as is BB (but not GG).

Yes, we know there can't be two girls. However our real options, each of 50% probability are:

1- BB
2- A boy and a girl.

 

[beesonthewhatnow]

Yes, we know there can't be two girls. However our real options, each of 50% probability are:

1- BB
2- A boy and a girl.

Seriously, get a bag of coins

 

[fogbat]

Yes, we know there can't be two girls. However our real options, each of 50% probability are:

1- BB
2- A boy and a girl.

You're taking the piss, right?

 

[ymu]

Yes, we know there can't be two girls. However our real options, each of 50% probability are:

1- BB
2- A boy and a girl.

Where does the 50% probability come from?

I might die today, or I might not. Therefore the probability that I will die today is 50%.

 

[littlebabyjesus]

One is declared, but we don't know which one.

I may indeed have been captaining a failboat here.

 

[ymu]

One is declared, but we don't know which one.

I may indeed have been captaining a failboat here.

Hallelujah!

 

[beesonthewhatnow]

One is declared, but we don't know which one.

I may indeed have been captaining a failboat here.

 

[littlebabyjesus]

I have to make a fool of myself on Urban at least once a month.

It's a rule.

 

[Santino]

 

[Crispy]

I have to make a fool of myself on Urban at least once a month.

It's a rule.

I could just delete the thread

 

[bi0boy]

I still think you're all thick.

If one is a boy, and he's the oldest one, the younger one is either a girl (BG) or a boy (BB)

Howver if he's the youngest one, the older one is either a girl (GB) or a boy (BB)

So BB is actually twice a likely as BG or GB, since the Bs can be in two different orders.

That gives our options, given one child is a boy, as BB, BB(with the Bs the other way round), GB and BG.

The other child is just as likely to be a boy or a girl

 

[beesonthewhatnow]

I could just delete the thread

It needs to stand as a monument to when the Crispy shield of science fact got slightly dented.

 

[beesonthewhatnow]

I still think you're all thick.

If one is a boy, and he's the oldest one, the younger one is either a girl (BG) or a boy (BB)

Howver if he's the youngest one, the older one is either a girl (GB) or a boy (BB)

So BB is actually twice a likely as BG or GB, since the Bs can be in two different orders.

That gives our options, given one child is a boy, as BB, BB(with the Bs the other way round), GB and BG.

The other child is just as likely to be a boy or a girl

 

[Crispy]

I still think you're all thick.

If one is a boy, and he's the oldest one, the younger one is either a girl (BG) or a boy (BB)

Howver if he's the youngest one, the older one is either a girl (GB) or a boy (BB)

So BB is actually twice a likely as BG or GB, since the Bs can be in two different orders.

That gives our options, given one child is a boy, as BB, BB(with the Bs the other way round), GB and BG.

The other child is just as likely to be a boy or a girl

Get a deck of cards. Shuffle them, inverting each cut as you do, so that they are face up and face down, all intermingled.

Deal out pairs of cards. Discard all pairs that are both face down (should be 6-7 of them). You should have (roughly) 6 face up pairs and 13 mixed-face pairs

1 Boy, 1 Girl, is twice as likely as 2 Boys.

 

[innit]

I still think you're all thick.

If one is a boy, and he's the oldest one, the younger one is either a girl (BG) or a boy (BB)

Howver if he's the youngest one, the older one is either a girl (GB) or a boy (BB)

So BB is actually twice a likely as BG or GB, since the Bs can be in two different orders.

That gives our options, given one child is a boy, as BB, BB(with the Bs the other way round), GB and BG.

The other child is just as likely to be a boy or a girl

please say you are joking - I'm begging you!

 

[littlebabyjesus]

I could just delete the thread

What thread?

 

[fractionMan]

Oh shit.

The second part is not "What is the probability that the other child is a boy" but "What is the probability you have two boys?"

That's where we went wrong, LBJ.

Plane crashes into the mountain. No survivors.

how can the answer to these questions be different?

 

[Santino]

how can the answer to these questions be different?

It's the difference between:

1. What is the probability of a two-child family having two boys?

and

2. What is the probability of a two-child family having two boys, given that we already know one of them is a boy?

 

[ymu]

I still think you're all thick.

If one is a boy, and he's the oldest one, the younger one is either a girl (BG) or a boy (BB)

Howver if he's the youngest one, the older one is either a girl (GB) or a boy (BB)

So BB is actually twice a likely as BG or GB, since the Bs can be in two different orders.

That gives our options, given one child is a boy, as BB, BB(with the Bs the other way round), GB and BG.

The other child is just as likely to be a boy or a girl

You're not thinking about the probability of each outcome. Half of all two child families have a girl and a boy, the other half have either two boys or two girls. Of all the families which have at least one boy, 2/3 of them have a girl as well.

 

[Crispy]

What thread?

That thread where we both shone like beacons of intellectual clarity and everyone else took ages to get it, which is a shame cos I accidentally deleted it.

 

[ymu]

how can the answer to these questions be different?

They're not. Crispy failed at explaining his fail.

But we know what he meant, and he's back on form now.

 

[Santino]

Crispy, far left:

 

[bi0boy]

Ok, say in all these two-child families, the second child was just oozing out of the flaps and hadn't revealed it's bits yet.

If the family already had a boy, would the doctor say "oooh it's just coming out but there's only a 1/3 chance it will be a girl I'm afraid, because I've excluded the GG combination already"

 

[Crispy]

Ok, say in all these two-child families, the second child was just oozing out of the flaps and hadn't revealed it's bits yet.

If the family already had a boy, would the doctor say "oooh it's just coming out but there's only a 1/3 chance it will be a girl I'm afraid, because I've excluded the GG combination already"

but that's not the question being asked
(it's good to feel right again)

 

[strung out]

Ok, say in all these two-child families, the second child was just oozing out of the flaps and hadn't revealed it's bits yet.

If the family already had a boy, would the doctor say "oooh it's just coming out but there's only a 1/3 chance it will be a girl I'm afraid, because I've excluded the GG combination already"

you're mixing up the chance of a new born baby being a boy or a girl, with the chance that a two child family will have two boys

 

[ymu]

Ok, say in all these two-child families, the second child was just oozing out of the flaps and hadn't revealed it's bits yet.

If the family already had a boy, would the doctor say "oooh it's just coming out but there's only a 1/3 chance it will be a girl I'm afraid, because I've excluded the GG combination already"

No, because that's an entirely different question. And that's the whole point of this puzzle. Just like the plane on a conveyor belt - you have to work out what question you're answering first.

 

[beesonthewhatnow]

So, are we all in agreement now that the answer to the puzzle as stated in the OP is 13/27?

 

[strung out]

No, because that's an entirely different question. And that's the whole point of this puzzle. Just like the plane on a conveyor belt - you have to work out what question you're answering first.

what plane on a conveyor belt? explain this puzzle to me...