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# One Girl - One Boy

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## Question

Ok, so Teanchi and Beanchi are a married couple (dont ask me whose he and whose she)!

They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.

Assume safely that the porbability of each gender is 1/2.

Ofcourse its not 1/2 else would make it a lousy puzzle...

Ans: 1/3

This is a famous question in understanding conditional probability, which simply means that given some information you might be able to get a better estimate.

The following are possible combinations of two children that form a sample space in any earthly family:

Girl - Girl

Girl - Boy

Boy - Girl

Boy - Boy

Since we know one of the children is a girl, we will drop the Boy-Boy possibility from the sample space.

This leaves only three possibilities, one of which is two girls. Hence the probability is 1/3

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#### Popular Posts

Let mine be one more vote for itsclueless's correct (also, rational ) answer. The probability of the "other child" being a girl is 1/2. The answer offered by brainden.com is incorrect, and even th

Your simulation is flawed, specifically at the point where you query if( family.Child1 || family.Child2 ) The 'or' condition encapsulates the condition that the family has at least one girl, but

Did you get to the end of my post? I came to a very important conclusion, I think. Your program assumes that the parents randomly told us the gender of one of their children, which is perfectly logi

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I had not paid attention and was rushed, and thus I overlooked it.

If you find the time, try actually performing the experiment I laid out using coins. If thinking about this mathematically doesn't convince you, real world experience is sure to.

No matter what, the chances of a child being a boy or a girl will always be 50%.

A child, yes, meaning a particular child. But the riddle isn't asking about a particular child.

I believe what you are thinking is that the chances of the second child completing either "boy, boy", "boy, girl" or "girl, girl" is 33% chance. You ARE correct in this sense.

No. You are making the same mistake others have made. There are four possible combinations of two children:

BB

BG

GG

GB

If we know that at least one of them is a girl, there are three:

GG

GB

BG

But in the question of anything, absolutely any problem concerning the gender of a child, the chances will always be 50% - No matter what.

No, not "no matter what". With conditions, probabilities often change.

I believe what you are thinking is: A couple is having twins - And they do not wish to know the gender of the babies. There is a 33% chance for each that the babies will be either: A, boy, boy, B, girl, girl, C, boy, girl. I believe this is what you are thinking.

It is a 33% chance that the children, together, will be either A, B, or C.

There is a 25% chance of one specific combination, not 33%:

BB

GG

BG

GB

If you think the order of BG doesn't matter, it does. There is a 50% chance that there will be one child of each gender. There is a 25% chance the children will be GG and a 25% chance of BB. 33% never comes in to question.

That is the way that the Lord created humans to be born

That's an argument for "Others", so I won't get into that here.

Please also think about this: How could the chances be 33% chance of the second child being a boy or girl - When there is only 2 possible possibilities, a boy or a girl.

This has been answered many times in this thread. The probability of the second child being a girl is 1/2. As has been discussed, the riddle is not asking about the second child.

"They have two kids, one of them is a girl, what is the probability that the other kid is also a girl."

Knowing know that one of them is a girl, the distribution look like this:

GG

GB

BG

With the girl we already know exists having to be in one of the above situations, the other child has a 1/3 chance of also being a girl.

"They have two kids, what is the probability that their second kid is a girl.", the distribution would look like this:

GG

BB

GB

BG

The other child would have a 1/2 chance of being a girl.

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sajow4 wrote:

No matter what, the chances of a child being a boy or a girl will always be 50%.

A child, yes, meaning a particular child. But the riddle isn't asking about a particular child.

Yes, you are correct again. I am surely not a very intelligent person, and much rather enjoy reading these puzzles than trying to solve them, so I may make many mistakes (As I have).

sajow4 wrote:

But in the question of anything, absolutely any problem concerning the gender of a child, the chances will always be 50% - No matter what.

No, not "no matter what". With conditions, probabilities often change.

Yes, you are correct. In any normal sense, as in if the question had simply asked, what are the chances of the second child being a boy/girl, it would be 50%.

sajow4 wrote:

I believe what you are thinking is that the chances of the second child completing either "boy, boy", "boy, girl" or "girl, girl" is 33% chance. You ARE correct in this sense.

No. You are making the same mistake others have made. There are four possible combinations of two children:

BB

BG

GG

GB

If we know that at least one of them is a girl, there are three:

GG

GB

BG

I reread what you wrote a few times, and yess, I believe I am gaining on your perspective, or, rather, what my perspective should have been.

I had made the "33% mistake" because I had not included G being before B, eliminating the possiblity as I had done B before G, but that was not correct. By doing that, I had gotten 33%, 3 choices, instead of 4 choices which I should have had, getting a result of a 25% chance.

sajow4 wrote:

That is the way that the Lord created humans to be born

That's an argument for "Others", so I won't get into that here.

I do not agree, as I believe it is alright to do so, as it may offend someone to pray in a fast food resturaunt before eating, but I also respect other peoples' wishes, and so, if you create a forum on this matter, I would be glad to discuss it further there, if you would like.

This has been answered many times in this thread. The probability of the second child being a girl is 1/2. As has been discussed, the riddle is not asking about the second child.

"They have two kids, one of them is a girl, what is the probability that the other kid is also a girl."

Knowing know that one of them is a girl, the distribution look like this:

GG

GB

BG

With the girl we already know exists having to be in one of the above situations, the other child has a 1/3 chance of also being a girl.

"They have two kids, what is the probability that their second kid is a girl.", the distribution would look like this:

GG

BB

GB

BG

The other child would have a 1/2 chance of being a girl.

You are correct, but I think that better wording would be (The one concerning the "33% mistake") that there is a 25% chance that the combonation is boy/girl, boy/boy, etc.,

I had gotten confused because people stated that what are the chances of the second child being a boy/girl if the first child is a boy/girl. I think that better wording would be as in the first sentance of this paragraph, and as the second problem you mentioned was what I had been thinking the original problem was, and had misunderstood and messed up.

I apologize, but I am only human.

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I am surely not a very intelligent person

Bull! Do you think I or anyone else in this thread wasn't initially fooled when first hearing this riddle or similar ones? This happens to be one of my favorite riddles and it is so because the solution goes against 'common sense' until delving further. I don't know anything about you besides what I've seen on this board, but from that alone I can see you are underestimating yourself. If you're not very intelligent for not seeing the logic of the solution until spending some time with it, then put me right beside you on that list.

I apologize

No need for that. You're a good man, Charlie Brown. I hope you stick around.

Edit: Upon receiving new information, change that to, "You're a good young lady, Lucy Brown".

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You are very kind, and I apprecciate it very much. Thank you.

I am really not one to be called "smart". I just like talking "funny".

Was I correct in my answer?

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^ Yup, you're correct. Welcome to the 1/3 club.

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I'm glad I understand it now.

Thank you for helping me.

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Huzzah! The 1/3 Club grows stronger.... are there any enemies left to convert?

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Huzzah! The 1/3 Club grows stronger.... are there any enemies left to convert?

It's 1/4, Unreality.

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lol are you being serious or are you just joking?

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can you feel the hook getting set?

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I'm joking, silly.

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the girl loves to tease ...!

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I haven't read all of the posts.

I mean, there's 12 pages, am I expected to?

But Yeah, I think it is 1/2.

Because the first girl is already born. So the chances stay the same for the second.

I have a friend with 4 sisters and no brothers. I don't think probability chances depending on how many you already have.

If you were to say..

The couple were going to have 2 children, what is the probability that they'll both be female?

Then you could answer 1/3 or 1/4 or whatever...

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I can't believe this thread is still going... and here I am to add to it. Originally I was in the 50/50 camp. I've now seen the light - and hope to add to the many explanations as to why it's not 50%...

The probability of a child being a girl are always 50%. Everyone in the 50% camp keeps getting hung up on the fact that the odds of a chile being one sex or the other are 50%, and the sex of anyone else can't change that. However, that's not the question.

The question is what is the probabilty of another child being a girl if one of the children is a girl. We don't know whether the known girl is first or second born, and it doesn't matter. We just know one is a girl. So as so many have shown before me, of 4 possibilities: BB, BG, GB, GG - there are 3 possibilities where one child is a girl: GG, GB, BG. Only one of the 3 possibilities where one is a girl is the other also a girl - hence 1 in 3.

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I haven't read all of the posts.

I mean, there's 12 pages, am I expected to?

It might help you understand what the riddle is asking instead of bringing this beyond 12 pages. As PDR mentioned, what you go on to write is evidence that you don't.

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there are 3 possibilities where one child is a girl: GG, GB, BG.
I'll add the words all and equally likely to PDR's nice explanation.

And echo Martini's caveat that the puzzle writer's attempt to fool you often depends on your answering a question you presume is being asked.

For example,

They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.

All equally likely possibilities = GG, GB, BG. Favorables = GG. Answer = 1/3.

They have two kids, the oldest is a girl, what is the probability that the other kid is also a girl.

All equally likely possibilities = GG, GB. Favorables = GG. Answer = 1/2.

The possibilities must be equally likely; otherwise ...

I just bought a lottery ticket. What's the probability I will win?

All possibilities: It's a winning ticket, it's a losing ticket. Favorables: it's a winning ticket. Answer = 1/2

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The possibilities must be equally likely; otherwise ...

I have a sister, what's the probability that I'm also girl? 0%, 33%, 50% or 100%?

you're just gonna have to guess... and 50% of you will be wrong....

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Wait. It gets even tougher ...

I have no brothers.

What's the probability that either of my two sisters has a brother? or that they both do? [remember to multiply]

This must be the longest thread for a New Puzzle. Amazing.

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I think I've figured out the source of the debate. It's not probability, it's the English language.

"One of them" can be interpreted two different ways: "one particular one" or "any given one."

Imagine you are talking to the parent of two children:

First interpretation:

"Ok."

"Is it a girl?"

GG: "Yes"

"Is your other child a girl?"

"Yes"

GB: "Yes"

"Is your other child a girl?"

"No"

BG: "No"

BB: "No"

The probability is 1/2

Second interpretation:

"Is one of your children a girl?"

GG: "Yes"

"Is your other child a girl?"

"Yes"

GB: "Yes"

"Is your other child a girl?"

"No"

BG: "Yes"

"Is your other cihld a girl?"

"No"

BB: "No"

The probability is 1/3

They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.

All equally likely possibilities = GG, GB, BG. Favorables = GG. Answer = 1/3.

They have two kids, the oldest is a girl, what is the probability that the other kid is also a girl.

All equally likely possibilities = GG, GB. Favorables = GG. Answer = 1/2.

The first can be taken to mean something like the second... something like "They have two kids, at least one of them is a girl" would be unambiguous.

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I think I've figured out the source of the debate. It's not probability, it's the English language.

If you go over individual arguments in this thread for 1/2, you'll see that a misunderstanding of probability and 1/2 being the intuitive answer is the problem, not the English language.

"One of them" can be interpreted two different ways: "one particular one" or "any given one."

Imagine you are talking to the parent of two children:

First interpretation:

"Ok."

"Is it a girl?"

GG: "Yes"

"Is your other child a girl?"

"Yes"

GB: "Yes"

"Is your other child a girl?"

"No"

BG: "No"

BB: "No"

The probability is 1/2

Second interpretation:

"Is one of your children a girl?"

GG: "Yes"

"Is your other child a girl?"

"Yes"

GB: "Yes"

"Is your other child a girl?"

"No"

BG: "Yes"

"Is your other cihld a girl?"

"No"

BB: "No"

The probability is 1/3

The riddle does not ask about a scenario where one child is picked and a question is asked about the other one, nor do I see where anyone interpreted the riddle to be asking that and chose 1/2 . Here's the riddle:

They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.

Only three scenarios:

GG

GB

BG

The other is a girl only 1/3 of the time.

If we are to understand the riddle to be asking "at least one of them is a girl, there is only one correct answer: 1/3. If you look over the arguments given in the thread, even after it was explained that the riddle isn't talking about "one girl only" the 1/2 group still believed the answer was 1/2.

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yep. The probability changes.

The friend I mentioned earlier that had 4 sisters..

Well i just learned that before he was born, doctors said he had a 92% chance of being a girl.

Yeah...

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oh wait a moment

see, it's not entirely about chance

sure, three scenarios,

BB

BG

GG

looks like a 1/3 chance if god just randomly puts babies into people or whatever

(I dunno, I'm atheist You can yell at me and tell me I'm going to hell, I could care less)

but biology interferes with the gender

that's why the doctor said my friend had a 92% percent (or so) chance of being a girl, when all four of his sisters were uhh... girls

....right?

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but biology interferes with the gender

that's why the doctor said my friend had a 92% percent (or so) chance of being a girl, when all four of his sisters were uhh... girls

....right?

Nope. The chances of a couple conceiving a boy or a girl are the same regardless of how many children of a particular sex they had previously.

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then why did the doctor say that?

I'm not challenging you, I'm just confused

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Maybe your friend's parents are pulling his leg? Maybe the doc was pulling his parents' leg and he thought they knew he was joking? Maybe what he said was based on an ultrasound done early in pregnancy that wasn't definitive? All I can do is guess.

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