Critical Thinking puzzle.

[Mr. Jon Donnis]

Its 50% every time.
You cannot know what the other child would be, therefore it can only be a boy or a girl, so 50/50

I think its a silly puzzle

[asdfg]

The answer changes depending on how much information you're given.

If you know the birth order (e.g. the first child was a boy) then it's a 50:50 split that the other will be a boy or girl.

But if you don't know the birth order and simply know that at least one of the two children is a boy then it's a 33.33/66.67 split for boy/girl.

---

You can replicate this scenario using playing cards.

If you randomly deal two cards face down and then randomly look at one of them and note its colour. Then when you turn the other card over it will be the same colour 1/3 of the time and the opposite colour 2/3 of the time.

If you try it and do enough trials (say more than 20) you'll see the pattern emerge.

It's exactly analogous to the boy/girl problem.



There's also an interesting twist if you want to appear to be psychic! If you know a person has a child of one sex you can then say "and the other is [the opposite]" and you will be right 67% of the time rather than the expected 50% of the time. ;D


.

[Mr. Jon Donnis]

I still dont get it, the sex of the first child makes no difference to that of the second.
Each time is a new 50/50 guess.

How can you be right 67% of the time when the odds are only 50/50

[tomroberts]

The way I looked at it - not saying this is right, but in jigsaw's breakdown, the 4th option (girl - girl) is out. Of the 3 remaining options, the probability of the second child being a girl is 2/3 (or 0.67) and the probability of it being a boy is 1/3 (or 0.33)

So, twice as likely to be a girl than a boy.

[asdfg]

Jul 16, 2009 8:01:48 GMT Mr. Jon Donnis said:

I still dont get it, the sex of the first child makes no difference to that of the second.

Remember, you don't know the birth order, you only know that at least one child is a boy.

Jul 16, 2009 8:01:48 GMT Mr. Jon Donnis said:

Each time is a new 50/50 guess.

How can you be right 67% of the time when the odds are only 50/50

The other child can only be a boy or a girl, but given the info that I gave, it will be a girl 67% of the time.

The question is not about whether the child is male or female, it's about the frequency with which [boy-boy], [boy-girl], [girl-boy] and [girl-girl] pairings occur in the population of people with 2 children where at least one of them is a boy (in which case the [girl-girl] option is eliminated).

[Mr. Jon Donnis]

The question is not about whether the child is male or female, it's about the frequency with which [boy-boy], [boy-girl], [girl-boy] and [girl-girl] pairings occur in the population of people with 2 children where at least one of them is a boy (in which case the [girl-girl] option is eliminated).

That doesnt make sense.
You are over complicating the issue.
Every child has a 50% chance of being a boy, or a girl.
It doesnt matter if you have given birth to 9 girls, it doesnt matter if you know that fact, the 10th child still has only a 50/50 chance of being a boy.

There is no 67% nonsense.

I am reffering to your original question

[blackadder]

eventually you can see it, if you work with probability a lot.

[asdfg]

If we have a choice of red snooker balls and green snooker balls then a ball can only be red or green: a 50:50 choice (same as being a boy or a girl).

But...

If you put 2 red and 1 green balls in a bag and draw out one at random then you will get a red ball 2/3 (67%) of the time and a green ball 1/3 (33%) of the time - even though a ball can only be red or green!

It's about prior probability.

If you have a population of people with 2 kids at least one of which is a boy, 1/3 (33%) will have [boy-boy], 1/3 (33%) will have [boy-girl], and 1/3 (33%) will have [girl-boy].

So, 1/3 (33%) will have 2 boys and 2/3 (67%) will have a boy and a girl. This is the prior probability - it's the same as working with 2 red and 1 green ball.

That's why if you come across a person with 2 kids and at least one of them is a boy, there's a 67% chance that the other one will be a girl: because there are twice as many families with a boy and a girl than there are families with 2 boys.

[Mr. Jon Donnis]

Yes i understand tht John, i am talking about your original puzzle, there was no prior knowledge on that one, so the answer is 50/50

[theminx]

Jul 15, 2009 10:03:57 GMT The Legendary Barb said:

Fluffet in days gone bye the childrens names were not on the book.

The names used to be on the first page of the Child Benefit book

[fluffet]

Ok sort of getting it but with the knowledge we have in the question alone the woman has two children and one is a boy, there are only two possible correct combinations to choose from Ie Boy/Boy Boy/Girl , with the knowledge that one of them is a boy already we can rule out Girl/Girl . This still leaves a 50/50 choice between boy or girl ?
The 1/3 only comes into it when you start talking about the order of the birth which adds another option Ie boy/girl girl/boy boy/boy....but i still dont see completely how if we are only discussing the sex of a child born to a mother the sex of any of her other children matters when it comes to the actual choice available ?There is still only boy or girl regardless of all the other factors and math.
Id however get the idea of how the 1/3 comes about etc

[asdfg]

Jul 16, 2009 18:07:42 GMT Mr. Jon Donnis said:

Yes i understand tht John, i am talking about your original puzzle, there was no prior knowledge on that one, so the answer is 50/50

That's what the puzzle is about - working out the prior probability!

[asdfg]

Jul 17, 2009 5:24:21 GMT fluffet said:

Ok sort of getting it but with the knowledge we have in the question alone the woman has two children and one is a boy, there are only two possible correct combinations to choose from Ie Boy/Boy Boy/Girl , with the knowledge that one of them is a boy already we can rule out Girl/Girl . This still leaves a 50/50 choice between boy or girl ?
The 1/3 only comes into it when you start talking about the order of the birth which adds another option Ie boy/girl girl/boy boy/boy....but i still dont see completely how if we are only discussing the sex of a child born to a mother the sex of any of her other children matters when it comes to the actual choice available ?There is still only boy or girl regardless of all the other factors and math.
Id however get the idea of how the 1/3 comes about etc

It's the other way round - if you know the birth order then the likelihood of the other being a boy or girl is 50:50. It's when you don't know the birth order that it becomes 33/67.

And remember, this is not about whether the other child is a boy or a girl; it's about how confident we can be about knowing whether the other child is a boy or a girl.

[Mr. Jon Donnis]

i think too much thought is going on.
At the end of the day it can only be a boy or a girl, and thats 50/50 regardless of prior knowledge

[asdfg]

Jul 17, 2009 19:22:56 GMT Mr. Jon Donnis said:

i think too much thought is going on.
At the end of the day it can only be a boy or a girl, and thats 50/50 regardless of prior knowledge

Buy a lottery ticket and can either win or lose - but the odds are not 50:50 because of prior probability.

This is the same thing.

[Mr. Jon Donnis]

No you either win or lose.
Odds come into it when you see how many numbers you can get, and in the lottery you are talking about 49 numbers, and you choose 6 of them.

In the puzzles case there is only 2 to pick from, so that makes it 50/50

[Amaris]

With the boy/girl question, the sperm decides the sex of the child, the female ova is x (female) and the sperm carries x & y (male) surely the sex of the child would depend on the strength of the individual sperm...so really I'm still unsure of the logic in the answer.

I will await the intellectual reply but I'm sure I will still be in the dark

[Amaris]

Ok I've been told that there are more girls born than boys so it gives the probability of it being a girl a higher percentage

[The Legendary Barb]

Who thinks up these questions, and have they nothing better to do with their time. Unless of course they are paid vasts amount of money to do so.

[bobdezon]

The correct answer is not always the obvious answer barb. That is the whole point of a critical thinking excercise. Think of it like a trick question, the trick being that if you apply logic and not "common sense" (which is usually not common or sensible) you will arrive at the correct answer.