A woman has two kids. One is a boy. What are the odds the other is a boy?

A woman has two kids. One is a boy. What are the odds the other is a boy? - Printable Version

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A woman has two kids. One is a boy. What are the odds the other is a boy? - TheSmartGuy - 2009-03-12

You flip a coin and there's a 50% chance that you'll flip a heads, whether this is your first flip or your 538th flip. So 50%.

A woman has two kids. One is a boy. What are the odds the other is a boy? - Mark - 2009-03-12

>"You flip a coin and there's a 50% chance that you'll flip a heads, whether this is your first flip or your 538th flip. So 50%."

>TheSmartGuy

laughingelfman.jpg

A woman has two kids. One is a boy. What are the odds the other is a boy? - Spaz - 2009-03-12

Read the question carefully, guys. It doesn't say "the first kid is a boy", it just says one is. These are the 4 possibilities, with equal probability, without knowing anything other than there are 2 kids:

BB
BG
GB
GG

If the question did say "the first kid is a boy" then it would be:

BB
BG
GB
GG

And it would be 50% chance of the other being a boy. But it doesn't say that, it just says one of the two is a boy. That makes it:

BB
BG
GB
GG

and therefore 33% chance of them both being boys.

Anyone want to make a post about the birthday paradox? Goggleemoticon

A woman has two kids. One is a boy. What are the odds the other is a boy? - Heidi - 2009-03-12

Spaz Wrote:Read the question carefully, guys. It doesn't say "the first kid is a boy", it just says one is. These are the 4 possibilities, with equal probability, without knowing anything other than there are 2 kids:

BB
BG
GB
GG

If the question did say "the first kid is a boy" then it would be:

BB
BG
GB
GG

And it would be 50% chance of the other being a boy. But it doesn't say that, it just says one of the two is a boy. That makes it:

BB
BG
GB
GG

and therefore 33% chance of them both being boys.

Anyone want to make a post about the birthday paradox?

Yes, it says 1 of them is a boy. The question is reffering to the "other" one, so doesn't that mean that it is reffering to the one that isn't a boy? It doesn't matter if it is the 1st or 2nd that is definitly a boy, my arguement of the question reffering to the other one still holds.

A woman has two kids. One is a boy. What are the odds the other is a boy? - JoeTang - 2009-03-12

ITT: Bad math.
This isn't the three prisoners problem. It's a poorly worded attempt at it though. The entire basis of the problem is that the choices are unknown, and a choice is made whilst this is true. Then, one answer is revealed and you are given a chance to make a second choice.

A woman has two kids. One is a boy. What are the odds the other is a boy? - Heidi - 2009-03-12

Ohhhhhhh I get it.

Yeah, I think it's 33%

Tongue

Seriously... anybody that ever comes up with horrible trick math questions... I hate them. They catch me out every time Sad

A woman has two kids. One is a boy. What are the odds the other is a boy? - IllegallySane - 2009-03-12

Wait, pineapple. I change my vote to 50%. Picked 33% accidentally.

Frown

I'm taking the simple approach and reading the question for what it is. It's not rocket science. The BB/BG/GB choices have nothing to do with the odds of the 2nd kid being a boy. It only matters if we didn't know what the first choice is, and we're asked the odds of a set event (2 are boys, 1st is a boy 2nd is a girl, 1st is a girl 2nd is a boy). We are only concentrating on the 2nd kid as an independent event. The odds of the 2nd kid being a boy is NOT dependent on the first kid. It's not what are the odds of the kids being boy/boy, or the odds of at least one boy. It's simply what are the odds that the other kid is a boy.

50% is 50%, or if we want to be really nit-picky, they say the odds of a boy is closer to 51% than 50%. Can't remember the reasoning behind it though.

*Besides, 33% is the correct answer IF the question was worded this way: A woman has two kids. One is a boy. What are the odds BOTH are boys? Opeth is only asking about the other kid being a boy.

A woman has two kids. One is a boy. What are the odds the other is a boy? - ShadyPriest - 2009-03-12

Spaz Wrote:Read the question carefully, guys. It doesn't say "the first kid is a boy", it just says one is. These are the 4 possibilities, with equal probability, without knowing anything other than there are 2 kids:

BB
BG
GB
GG

If the question did say "the first kid is a boy" then it would be:

BB
BG
GB
GG

And it would be 50% chance of the other being a boy. But it doesn't say that, it just says one of the two is a boy. That makes it:

BB
BG
GB
GG

and therefore 33% chance of them both being boys.

Anyone want to make a post about the birthday paradox?

-nvm-

A woman has two kids. One is a boy. What are the odds the other is a boy? - crewe127 - 2009-03-12

It's 97% cause i said so...beeeeeeeeeeeeeeeeeeeeaaaaaaaaaaach

A woman has two kids. One is a boy. What are the odds the other is a boy? - GummyBear - 2009-03-12

It just depends on which point of view you're looking at, which makes up the condition for this probability question.

A woman has two kids. One is a boy. What are the odds the other is a boy? - DarkPwnage - 2009-03-13

Is this like statistics mumbo-jumbo or something that everyone is saying? It makes about as much sense as that scene from 21 with the 3 doors and he says that his odds of having the right door after one of the 3 is revealed is then magically 66%.

I guess Calculus doesn't help with understanding beyond the most basic probability.

A woman has two kids. One is a boy. What are the odds the other is a boy? - IllegallySane - 2009-03-13

GummyBear Wrote:It just depends on which point of view you're looking at, which makes up the condition for this probability question.

I doubt it's a probability question. It only SOUNDS like a probability question. The thread feels like this right now:

[YOUTUBE]poncZ1K9Tio[/YOUTUBE]

A woman has two kids. One is a boy. What are the odds the other is a boy? - GummyBear - 2009-03-13

DarkPwnage Wrote:Is this like statistics mumbo-jumbo or something that everyone is saying? It makes about as much sense as that scene from 21 with the 3 doors and he says that his odds of having the right door after one of the 3 is revealed is then magically 66%.

I guess Calculus doesn't help with understanding beyond the most basic probability.

Well, given 3 doors, 2 are empty, 1 has a prize, when you're picking the door, your odd is 1/3 of getting the prize.

When a door has been revealed, as empty, your odd is still 1/3, because when you picked that door, that's your odd.

If you get to re-pick, your odd will be 1/2. Since you get to swap, your odd is now the reverse of what you had before, ie 2/3.

That's conditional probability. When you make your choice, that's your odd. Knowing further information without allowing you to make a choice does NOT improve your odds.

There's a game calls "deal or no deal" in Australia, the idea is you have 26 suitcases, and you pick 1 at the start and there's an eliminating process. The max prize is 200k. Your odd at getting the 200K is 1/26 even if there're 5 suitcases left and the 200K is still available.

In the baby situation, if you're looking at the point of view of the babies, then each baby has a 1/2 chance of becoming a boy. If you're looking at it from the point of view of the mother, giving birth to 2 babies, the nurse tells her one of them is a boy, then, statistically, to the mother, the next announcement from the nurse has 1/3 chances that she'll get another boy.

Nowaday, they go get ultra-sounds tho.

A woman has two kids. One is a boy. What are the odds the other is a boy? - DeadHead - 2009-03-13

The way you asked the question is too ambiguous.

There are two ways to interpret this.

1)
A women has a child. It's a boy.
A woman has another child. What gender is it?

Since those are two independent events, there is (non-biologically speaking), a 50% chance of having a male or female child

and

2)
The way you actually meant you question to be phrased.

I suggest next time you phrase it better so there is no ambiguity.

A woman has two kids. One is a boy. What are the odds the other is a boy? - Nikkey - 2009-03-13

IllegallySane Wrote:*Besides, 33% is the correct answer IF the question was worded this way: A woman has two kids. One is a boy. What are the odds BOTH are boys? Opeth is only asking about the other kid being a boy.

But if one of the kids is a boy, and the other one is a boy, then both are boys.

A woman has two kids. One is a boy. What are the odds the other is a boy? - Tir - 2009-03-13

And therein lies the ambiguity.

A woman has two kids. One is a boy. What are the odds the other is a boy? - GummyBear - 2009-03-13

IllegallySane Wrote:*Besides, 33% is the correct answer IF the question was worded this way: A woman has two kids. One is a boy. What are the odds BOTH are boys? Opeth is only asking about the other kid being a boy.

Hmm, interesting. I am wondering, if you already know one is a boy, then the next kid is a boy has 50% chance?

Its like you flipped a head, what's the odd that the next one is a head also? That's 50% chance. Goggleemoticon

A woman has two kids. One is a boy. What are the odds the other is a boy? - shouri - 2009-03-13

Peoples, go back to page 3. Follow the link, and learn to read. Its 33%.

One of them is a boy. For the other to also be a boy you'd need the scenario BB.

Out of four choices
BB
GB
BG
GG <- this one is gone automatically.

GB and BG are not the same since you don't know which kid is which. You're not allowed to assume that the OLDER kid is the boy (GB) or that the YOUNGER kid is the boy (BG).

If, and only if, you're told which kid is the boy, then it turns out to be 50%.
Ex. If you know the older kid is the boy
BB
GB
BG <- goes away
GG <-goes away

50% chance of the other kid being a boy too

Same applies if you know the younger child is a boy.

BUT you dont know that >>

Thus GB & BG have to be treated separately.

Case in point, three posibilities that you are ALL overly complicating:

BB
GB
BG

1/3 chance of 1 kid being a boy AND the other kid being a boy (BB)

Done. nothing else. no more. gtfo with intuition, it doesn't always work. There's a TON more math concepts that intuition will fail with. And if you guys aren't able to look past your first instinct you will fail upper division math classes in college. Take this from a math major.

A woman has two kids. One is a boy. What are the odds the other is a boy? - Nikkey - 2009-03-13

GummyBear Wrote:Hmm, interesting. I am wondering, if you already know one is a boy, then the next kid is a boy has 50% chance?

Its like you flipped a head, what's the odd that the next one is a head also? That's 50% chance.

You can't do it that way. Sigh..

You flip two coins. We know that one of them is head. What is the chance the other is head as well?

We already know that we have double the chance of getting a head and a tail than getting two heads, because this would be the output if we had all combinations:

HH
HT
TH
TT

And so forth. Read upper post for more elaboration.

A woman has two kids. One is a boy. What are the odds the other is a boy? - Alloy - 2009-03-13

This thread has reached the maximum paradoxical limit. Time to blow this all up.

Start at the botom if you are bored :p

Yes, I got bored, and drew it all.