A simple logic problem

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A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?
 

Rx God
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I'm thinking 4 possibilities

BG
GB
BB
GG

GG possibility is gone, but G is still live in 2 of 3 scenarios remaining.
 
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I'm thinking 4 possibilities

BG
GB
BB
GG

GG possibility is gone, but G is still live in 2 of 3 scenarios remaining.

We are just trying to find out what the other child is KNOWING 1 child is a boy...so your first 2 are the same thing...does it matter that B came before G or G came before B...so take that away..or put it into 1 so you have...

BG
BB

I thought this was fairly easy. Its either a girl or boy...1 outta 2...50%.


:grandmais
 

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50% in my book. Other child should be independent of the possibilities that exist considering both children.
 

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BG and GB end up the same thing, but they each have a 25% chance of happening...that's why he separated them out.

so you could combine them into BG, but you'd have to give it a 50% weight
 

Rx God
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I'm not certain I'm correct.

4 possibilites to start.

You know he doesn't have two girls, but could have:

First born daughter, first born son

or

another son

Isn't Girl 2/3 ?
 
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I'm not certain I'm correct.

4 possibilites to start.

You know he doesn't have two girls, but could have:

First born daughter, first born son

or

another son

Isn't Girl 2/3 ?


Doug, Look at it this way......


I bump into you at the store...

ME: Hey doug, haven't seen ya in a long time...did I tell you I have 2 kids now...ya my son is doing great in baseball. Oh hey, I gotta run...my wife is making dinner...give me a call sometime, well talk...

There you are left standing...and the other kid could either be a boy or a girl....50/50 chance of either.
 

You cant win unless you learn how to lose
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"He does not tell you whether the son is the oldest child or the youngest child"
is only put in to throw one of
 

Oh boy!
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I'm thinking 4 possibilities

BG
GB
BB
GG

GG possibility is gone, but G is still live in 2 of 3 scenarios remaining.

Doug,

I like the way you think. However, I have a different way of looking at things. I may be wrong in the way I look at things but here goes.

Before we know the gender of either child your possibilities are valid. However, once the gender of one child is known then the probability of the gender of the other child should be based upon what is not known. It can no longer be based upon the original possibilities. Therefore the probabilities must be made based upon the 1 child that is left.
 

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Just to completely throw everyone off with my twisted way of thinking, is a father that has a son with one woman any more likely to have another son (as opposed to a daughter) with the same woman?

Yeah, I know, totally not the aim of the question but I like to complicate things.
 

Rx God
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A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?

........................................................................................................

I'll change my answer to 100%

It's a trick question.

The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.
 

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Just to completely throw everyone off with my twisted way of thinking, is a father that has a son with one woman any more likely to have another son (as opposed to a daughter) with the same woman?

Yeah, I know, totally not the aim of the question but I like to complicate things.

logically no, IMO

However the family that lived next to me as a kid, had seven sons, then finally a daughter.

There could be some bias within families ?

Do people with six kids have 3B and 3G near the expected 50% ?
 

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A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?

........................................................................................................

I'll change my answer to 100%

It's a trick question.

The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.

It doesn't automatically imply that based upon how it is worded. For example, if the guy has a son named Tom and a son named Bill, he could talk about his son Tom. That would fit the conditions talking about his son.

It also doesn't say that he explicitly mentions the word "his son". It just mentions he is talking about the boy.
 

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This is not a trick question. The man just happened to only talk about the son. And there is no bias towards having a male or female in the problem. I love the discussion, and will give the answer in the morning.
 

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A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?

........................................................................................................

I'll change my answer to 100%

It's a trick question.

The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.

Doug, for simplicity's sake, pretend the question is re-worded as saying "The man tells you about his son Billy." That way there are no implications as to the gender of the other child.
 
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I knew I saw this before............Here is the Rundown
As the answer could be Both 2/3 or 1/2

Supposing that we randomly pick a _child_ from a two-child family. We
see that he is a boy, and want to find out whether his sibling is a
brother or a sister. (For example, from all the children of two-child
families, we select a child at random who happens to be a boy.) In
this case, an unambiguous statement of the question could be:

From the set of all families with two children, a child is
selected at random and is found to be a boy. What is the
probability that the other child of the family is a girl?

Note that here we have a pool of kids (all of whom are from two-child
families) and we're pulling one kid out of the pool. This is like the
problem you're talking about. The child selected could have an older
brother, an older sister, a younger brother or a younger sister.

Let's look at the possible combinations of two children. We'll use B
for Boy and G for girl, and for each combination we'll list the older
child first, so GB means older sister while BG means younger sister.
There are 4 possible combinations:

{BB, BG, GB, GG}

From these possible combinations, we can eliminate the GG combination
since we know that one child is a boy. The three remaining possible
combinations are:

{BB, BG, GB}

In these combinations there are four boys, of whom we have chosen one.
Let's identify them from left to right as B1, B2, B3 and B4. So we
have:

{B1B2, B3G, GB4}

Of these four boys, only B3 and B4 have a sister, so our chance of
randomly picking one of these boys is 2 in 4, and the probability is
1/2 - as you have indicated.


But now let's look at a different way of selecting the "boy" in the
problem. Suppose we randomly choose the two-child _family_ first. Once
the family has been selected, we determine that at least one child is
a boy. (For example, from all the mothers with two children, we select
one and ask her whether she has at least one son.) In this case, an
unambiguous statement of the question could be:

From the set of all families with two children, a family is
selected at random and is found to have a boy. What is the
probability that the other child of the family is a girl?

Note that here we have a pool of families (all of whom are two-child
families) and we're pulling one family out of the pool. Once we've
selected the family, we determine that there is, in fact, at least one
boy.

Since we're told that one child (we don't know which) is a boy, we can
eliminate the GG combination. Thus, our remaining possible
combinations are:

{BB, BG, GB}

Each of these combinations is still equally likely because we picked
one of the four families.

Now we want to count the combinations in which the "other" child is a
girl. There are two such combinations: BG and GB.

Since there are three combinations of possible families, and in two of
them one child is a girl, the probability is 2/3.
 

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logically no, IMO

However the family that lived next to me as a kid, had seven sons, then finally a daughter.

There could be some bias within families ?

Do people with six kids have 3B and 3G near the expected 50% ?

actually the expected % for 3 of each would be 20/64=31.25%
 

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