The boy-girl puzzle

As an alternative to the old plane-conveyor one…

You ask a woman how many children she has and she says two.
Then for some odd reason you ask her “Is at least one a girl?”, to which she replies “Yes”.

So what are the odds that she has a girl and a boy?

(to avoid some argument: assume this is a perfect world where the odds of boy or girl conception are 50/50 and that there are no genetic “third sex” possibilities)

fish

66%

Next…

75/25. Not sure how on earth you got 66% 😛

Explanations are just so passe don’t ya know…

And for a bonus point, what would the odds be if you had instead asked “Tell me sex of one of them” and she had said “A girl”?

(probably best to stick with percentage odds for those of us that can’t do fractions)

50%

And next…

Why aren’t you asleep and tucked up in bed?

One could ask the same question… 😉

But I am in bed at least, just wish I could sleep…

50%, 1/2, half, whatever you want to call it.

People, for once and all, something that has already happened (in this case the sex of one child has been announced) CAN NOT EVER influence the probability of something happening in the future.

As we know one child is a girl, the options in this case are thus:

Girl + Girl
Girl + Boy

As the first child being a girl DOES NOT influence the probability of the 2nd child’s sex, and the quoted probability of any further child being 50/50, then this is the probability of there being a boy and a girl.

funkynick, how the hell did you get 66%? Did you pay attention to maths lessons in school?

jarl, same comment as for funkynick.

God why don’t people understand probability! ARGH!!! I have presented to some very high level people in big corporations, on large salaries several times talking about probability, and almost without exception they NEVER seem to understand that the fact that an event has happened (ie. flipping a coin, the sex of a child etc etc.) DOES NOT influence any upcoming events!

You flip a coin 4 times in a row, you get 4 straight heads. What’s the probability of getting a head on the 5th attempt?

Answer is it’s 50%, unless you have a 2 headed coin, in which case it would be 100% 😉

Though don’t confuse this with working out the probability of flipping 5 straight heads (on a coin with a heads and a tails on it) before any flipping occurs. This would of course be 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32 (or 0.03125 for those that only do decimals).

Oh, and as for the plane on a conveyor, the wheels on a plane have nothing to do with its ability to take off or not. Air speed over the wings is what matters!

mboy, I suspect you need to review your grasp of probability.

The subtley lies in that the children are not the same child.
By the question “is at least one of them a girl”, you allow for the chance that this could refer to either of them. We aren’t dealing with probability of future events, as in your coin toss example, but of a predefined existing situation.

If we only knew that she had 2 children, we’d have the following possibilities:

Boy/Girl
Boy/Boy
Girl/Boy
Girl/Girl

As we know that at least one is a girl, it rules out the Boy/Boy scenario.
Of the scenarios we have left, two involve one boy, and one girl. Resulting in a chance of 2 thirds.

Aidy

That’ll learn me to read the subtleties of the question! 😳

Yes sorry, pre-defined existing situation is indeed totally different.

Apologies to funkynick too in that case.

Maths/probability is/was my strong point, my understanding of verbal reasoning has never been quite so strong.

Well worded question GrahamS! Caught me napping at least.

sex of the offspring is highly influenced by enviromental factors. where does she live?

No worries mboy… now I wonder if there is a smug smiley? 😉

Bunnyhop – Member

Why aren’t you asleep and tucked up in bed?

How’s the snow?

If we only knew that she had 2 children, we’d have the following possibilities:

Boy/Girl
Boy/Boy
Girl/Boy
Girl/Girl

As we know that at least one is a girl, it rules out the Boy/Boy scenario.
Of the scenarios we have left, two involve one boy, and one girl. Resulting in a chance of 2 thirds.

Surely in this situation Boy/Girl is the same as Girl/Boy? The question doesn’t place any importance on the order of the children so if ‘at least one is a girl’ the only possibility for the other child is to be either a boy or a girl. We know this is a 50/50 chance.

Although I last did maths in anger over 10 years ago and I’m quite hungover this morning so I might be spouting rubbish.

I can’t see why the order matters either so there only 2 possible combinations.

But then isnt the probability of “a boy/girl combo, in any order” higher than boy boy or girl girl, twice as high, so the maths still works out?

I can’t see why the order matters either so there only 2 possible combinations.

The order does matter. The youngest being a boy and the oldest being a girl is a different scenario from the youngest being a girl and the oldest being a boy.

So that gets us back to Aidy’s 4 possibilities:

Youngest/Oldest

Boy/Girl
Boy/Boy
Girl/Boy
Girl/Girl

Boy/Boy is excluded so the probability is 2/3rds

And so it begins….

50:50 end of. Any other solution is just stupid.

Is one one a girl? Yes. Is the other one a boy? 50:50 chance.

Oh, and as for the plane on a conveyor, the wheels on a plane have nothing to do with its ability to take off or not. Air speed over the wings is what matters!

You’re correct on both of those. But that still doesn’t answer whether or not it takes off. I want to know what, because I’d love it to turn out that you’re useless with physics as well as verbal reasoning after your rant about people not understanding probability above 🙂

The original question said nothing about order that they came in just that she has two and one of them is a girl.

so…
girl/boy
boy/girl are the same in this instance, surly it’s 50/50

Is one one a girl? Yes. Is the other one a boy? 50:50 chance

Maybe you should read the question again?

mike – tell me what i missed.

The order does matter. The youngest being a boy and the oldest being a girl is a different scenario from the youngest being a girl and the oldest being a boy.

No one asked about the age.

mike – tell me what i missed.

The question asks if “AT LEAST one is a girl”.

That means you can have 3 out of the 4 possible combinations. The question didnt ask:

Which one comes first?
If the first is an X, whats the second?
How many cows does it take to provide enough milk for the family?

etc

Oh, and as for the plane on a conveyor…

DON’T CROSS THE STREAMS!

And for completeness, planes only take off due to airspeed over the wings, so the plane still has to reach the same take-off speed and the conveyor makes no difference (assuming no friction in the bearings/wheels) to what the engine has to do.

Who gives a shit which comes first? The question doesn’t ask that.

Smee… I’m sure the children do! 😀

Dad usually, though if he’s a gentleman then it could be mum 😮

Yep funkynick knows his stuff.

The correct answer is of course 66% (well 66.6666..% actually but you get the point)
And in the second bonus question the answer is 50%.

Anything else is wrong wrong wrong.

Woooot.. do I get a prize? 😀

My head hurts.

You know she has 2 kids.
She states at least one is a girl.

So the other must be either boy or girl (50% chance). We ask whats the odds she has a girl and a boy, the answer is 50% because we already know one (at least) is a girl and we know the probability of a single event and only want one of the two possible outcomes.

I used to like probability problems, but this has me confused.

As for the bonus point, I dont see it makes any difference, youve still effectively ascertained that one is a girl and the other could be either?

More detailed explanation needed

I’m still lost why it’s 66% as the order was never discussed it only if you specify the order will the odds change surely?

I’m sure what we are after here is some baysian analysis..

Related point:

Given a group of parents with two children then 75% of them will have at least one girl. But in that same group, 75% will also have at least one boy!

Discused here the ambiguity also seems to be with how the question is asked.

I’m bored now, explanation of the original point or **** off 🙂