oldest.girl, revisited
r...@perforce.com
figure out the flaw in my thinking and let me know where it is.
I recently revisited the 'oldest.girl' problem. Here's the statement
of the problem from the archives:
You meet a stranger on the street, and ask how many children he
has. He truthfully says two. You ask "Is the older one a girl?"
He truthfully says yes. What is the probability that both children
are girls? What would the probability be if your second question had
been "Is at least one of them a girl?", with the other conditions
unchanged?
and the solution is posted as:
There are four possibilities:
Oldest child Youngest child
1. Girl Girl
2. Girl Boy
3. Boy Girl
4. Boy Boy
If your friend says "My oldest child is a girl," he has eliminated
cases 3 and 4, and in the remaining cases both are girls 1/2 of the
time. If your friend says "At least one of my children is a girl,"
he has eliminated case 4 only, and in the remaining cases both are
girls 1/3 of the time.
All well and good. I recently saw the puzzle posted slightly differently;
here was the puzzle statement:
(a) A woman has two children. She is standing in front of you with one
of them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do". What is the probability that
her other child is a boy?
(b) A woman has two children. She is standing in front of you with one of
them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do. My husband took our baby to
the zoo." What is the probability that her other child is a boy?
This seems to me to be the same puzzle, with the answer to (a) being 2/3,
and the answer to (b) being 1/2. (Is it the same as the puzzle in the archive?
If not, you don't need to read any further... but please tell me why it's not
the same).
So let's assume that it is the same puzzle; the answer to the first
question is 2/3 and the answer to the second is 1/2. What I'm going to
do here is move the second question in the direction of the
first by gradually rewording it. What I can't figure out is: at what
point does the answer to this gradually-evolving question 'change' from
1/2 to 1/3, and why?
(1) A woman has two children. She is standing in front of you with one of
them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do. My husband took our baby to the
zoo." What is the probability that her other child is a boy? (answer: 2/3)
(2a) A woman has two children. She is standing in front of you with one of
them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do. My husband took our youngest to
the zoo." What is the probability that her other child is a boy?
(2b) A woman has two children. She is standing in front of you with one of
them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do. My husband took our oldest to
the zoo." What is the probability that her other child is a boy?
(3) A woman has two children. She is standing in front of you with one of
them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do. My husband took our 'stromest' to
the zoo." The woman is foreign, and you know that 'stromest' means either
'youngest' or 'oldest', but you don't know which. What is the probability
that her other child is a boy?
(4) A woman has two children. She is standing in front of you with one of
them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do". You ask "Is your second
child either younger or older then this child?", and she says, with
a puzzled look on her face, "of course!" What is the probability that
her other child is a boy?
(5) A woman has two children. She is standing in front of you with one
of them -- her ten-year-old daughter. You say to her, "I know you have two
children." She responds, truthfully, "I do". What is the probability that
her other child is a boy? (answer: 1/2)
My question is: at which question does the answer to the question change?
And why?
(It seems to me that the answer has to be one of the following:
A) The version of the puzzle that I provided is NOT the same as the archived
version; or
B) The puzzle as stated at (3) above is fundamentally different then combining
(2a) and (2b). If so, I don't see it: the answer to 2a is 1/2; the answer
to 2b is 1/2; there's a 50% chance of her saying 2a and a 50% chance
of her saying 2b; and (50% * 1/2) + (50% * 1/2) is 1/2, which would seem
to be the answer to (3).
)
Anway, thanks in advance. This is driving me crazy.
Robert Orenstein
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Matthew T. Russotto
}HHi, all. This is a rather long posting; I'm hoping that someone can
}figure out the flaw in my thinking and let me know where it is.
}
}I recently revisited the 'oldest.girl' problem. Here's the statement
}of the problem from the archives:
}All well and good. I recently saw the puzzle posted slightly differently;
}here was the puzzle statement:
}
} (a) A woman has two children. She is standing in front of you with one
} of them -- her ten-year-old daughter. You say to her, "I know you have two
} children." She responds, truthfully, "I do". What is the probability that
} her other child is a boy?
}
} (b) A woman has two children. She is standing in front of you with one of
} them -- her ten-year-old daughter. You say to her, "I know you have two
} children." She responds, truthfully, "I do. My husband took our baby to
} the zoo." What is the probability that her other child is a boy?
}
}This seems to me to be the same puzzle, with the answer to (a) being 2/3,
}and the answer to (b) being 1/2. (Is it the same as the puzzle in the archive?
}If not, you don't need to read any further... but please tell me why it's not
}the same).
It's not the same. In both cases above, a girl child has been
identified (the one right in front of you is a girl), and that's
sufficient to make the probability that the other child is a boy 1/2.
--
Matthew T. Russotto russ...@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."
bbarth...@voltdelta.com
> them -- her ten-year-old daughter. You say to her, "I know you have two
> children." She responds, truthfully, "I do. My husband took our baby to the
> zoo." What is the probability that her other child is a boy? (answer: 2/3)
>
the problem never changes the answer, it was 1/2 from the beginning. To see
why this is so, take the table that you posted and substitute "This" for
"Oldest" and "Other" for "Youngest".
This child Other child
1. Girl Girl
2. Girl Boy
3. Boy Girl
4. Boy Boy
>
> (It seems to me that the answer has to be one of the following:
>
> A) The version of the puzzle that I provided is NOT the same as the archived
> version; or
Bingo.
>
Bruce Bartholomew
Riverside, CA
Matt Folwell
[snip "oldest child" puzzle]
> (a) A woman has two children. She is standing in front of you with one
> of them -- her ten-year-old daughter. You say to her, "I know you have two
> children." She responds, truthfully, "I do". What is the probability that
> her other child is a boy?
>
> (b) A woman has two children. She is standing in front of you with one of
> them -- her ten-year-old daughter. You say to her, "I know you have two
> children." She responds, truthfully, "I do. My husband took our baby to
> the zoo." What is the probability that her other child is a boy?
>
> This seems to me to be the same puzzle, with the answer to (a) being 2/3,
> and the answer to (b) being 1/2. (Is it the same as the puzzle in the archive?
This isn't the same puzzle. The answer to (a) is also 1/2.
If you replace "oldest" with "nearest to his/her mother" it becomes
clearer.
Or, to put it another way, if the woman has one son and one daughter,
half the time that you meet her she'll be with her son. In the puzzle
as stated in the archive, when you ask "Is one of your child a girl?"
(and there's one of each) the answer will always be yes, and not "one
of them's a boy"
I hope that's comprehensible.
Matt
--
Matt Folwell, P2 Whewell's Court, Trinity College, Cambridge. CB2 1TQ
mj...@cam.ac.uk
David K. Lewis
> In article <79m5fh$e9q$1...@nnrp1.dejanews.com>, <r...@perforce.com> wrote:
> }figure out the flaw in my thinking and let me know where it is.
> }
> }I recently revisited the 'oldest.girl' problem. Here's the statement
> }of the problem from the archives:
> [...]
> }All well and good. I recently saw the puzzle posted slightly differently;
> }here was the puzzle statement:
> }
> } of them -- her ten-year-old daughter. You say to her, "I know you have two
> } children." She responds, truthfully, "I do". What is the probability that
> } her other child is a boy?
The probability here is 2/3.
> } (b) A woman has two children. She is standing in front of you with one of
> } them -- her ten-year-old daughter. You say to her, "I know you have two
> } children." She responds, truthfully, "I do. My husband took our baby to
> } the zoo." What is the probability that her other child is a boy?
The probability here is 1/2
> }This seems to me to be the same puzzle, with the answer to (a) being 2/3,
> }and the answer to (b) being 1/2. (Is it the same as the puzzle in the archive?
> }If not, you don't need to read any further... but please tell me why it's not
> }the same).
>
> It's not the same. In both cases above, a girl child has been
> identified (the one right in front of you is a girl), and that's
> sufficient to make the probability that the other child is a boy 1/2.
IMO, this is not correct, the tree for 2 children (assuming equal chance
of b/g birth) is:
BB
GB
BG
GG
In the first example, we see a girl so the top row is eliminated from
consideration, but the bottom three remain since we don't know if the
child we are seeing is older or younger than her sibling. In 2 of the
3 remaining cases the other child is a Boy, so the probability is 2/3.
In the second example, we see a girl AND we know she is the oldest so
the top 2 rows are eliminated from consideration. In 1 of the remaining
2 cases the other child is a Boy, so the probability is 1/2.
As always any opinions I may have written above are mine and mine alone.
Dave.
Guy Steven
dk...@cas.org (David K. Lewis) writes:
> In article <MyEv2.502$0l2.7...@newshog.newsread.com>, russ...@wanda.vf.pond.com (Matthew T. Russotto) writes:
>> In article <79m5fh$e9q$1...@nnrp1.dejanews.com>, <r...@perforce.com> wrote:
>> }HHi, all. This is a rather long posting; I'm hoping that someone can
>> }figure out the flaw in my thinking and let me know where it is.
>> }
>> }I recently revisited the 'oldest.girl' problem. Here's the statement
>> }of the problem from the archives:
>> [...]
>> }All well and good. I recently saw the puzzle posted slightly differently;
>> }here was the puzzle statement:
>> }
>> } (a) A woman has two children. She is standing in front of you with one
>> } of them -- her ten-year-old daughter. You say to her, "I know you have two
>> } children." She responds, truthfully, "I do". What is the probability that
>> } her other child is a boy?
>
> The probability here is 2/3.
The probability is 1/2.
The standard boy girl tree is
BB
GB
BG
GG.
By knowing that there is one girl, we can eliminate line one. We have no
idea as to ages though, and so the choice is not from
GB,BG,GG but from GB,BG,GG,GG.
--
Guy Steven
15 Massey Crescent, Christchurch New Zealand
ph 355 6189
fax 355 6429
Matthew T. Russotto
It is 1/2, but not for the reasons you give. Ages have nothing to do
with it -- ANY characteristic which allows us to identify a girl is
sufficient to make the difference. In this case, it's the fact that
the girl is standing in front of you.
"The neighbor has two children, one light-haired and one dark-haired. The
dark haired one is a girl. What is the probability that the other is
a boy?" -- 1/2
"The neighbor has three children, one light-haired and two dark-haired. At
least one of the dark haired ones is a girl. What is the probability
that the other dark-haired one is a boy?" 2/3
"How about the light-haired one?" 1/2
"The neighbor has two children, the taller of which is a girl. What is
the probability that the shorter is a boy?" 1/2
"The neighbor has two children, one is the girl in that picture. What
is the probability that the other is a boy?" 1/2
"The neighbor has a set of identical twins, one of which is a girl.
What is the probability that the other is a girl?" 1
Seth Breidbart
Matthew T. Russotto <russ...@wanda.vf.pond.com> wrote:
>"The neighbor has two children, the taller of which is a girl. What is
>the probability that the shorter is a boy?" 1/2
I disagree. I bet if you asked the parents of all the kids in some
junior high school (say), if they had two children, and if the taller
one is a girl, whether the shorter one is also a girl, you wouldn't
get that close to 1/2 (as you would if you asked if the older one was
a girl).
Seth
Matthew T. Russotto
Because height and sex are not independent variables. Picky, picky.
Dr D F Holt
>Seth Breidbart <se...@panix.com> wrote:
>}In article <BKLv2.66$Rk.1...@newshog.newsread.com>,
>}Matthew T. Russotto <russ...@wanda.vf.pond.com> wrote:
>}
>}>"The neighbor has two children, the taller of which is a girl. What is
>}>the probability that the shorter is a boy?" 1/2
>}
>}I disagree. I bet if you asked the parents of all the kids in some
>}junior high school (say), if they had two children, and if the taller
>}one is a girl, whether the shorter one is also a girl, you wouldn't
>}get that close to 1/2 (as you would if you asked if the older one was
>}a girl).
>
>Because height and sex are not independent variables. Picky, picky.
Oh well, since we seem to be inundated with the two child problem yet
_again_, here is another very old one:
A man and woman have 9 children, all girls, and are expecting a new baby.
What is the probability that it will be another girl?
Derek Holt.
David A Karr
>A man and woman have 9 children, all girls, and are expecting a new baby.
>What is the probability that it will be another girl?
Based on my recollection of a slightly famous (in rec.puzzles)
scientific study, I'd guess the probability exceeds 1/2 by some
significant amount.
--
David A. Karr "Groups of guitars are on the way out, Mr. Epstein."
ka...@shore.net --Decca executive Dick Rowe, 1962
Matthew T. Russotto
Dr D F Holt <ma...@lily.csv.warwick.ac.uk> wrote:
}Oh well, since we seem to be inundated with the two child problem yet
}_again_, here is another very old one:
}
}A man and woman have 9 children, all girls, and are expecting a new baby.
}What is the probability that it will be another girl?
Gamblers fallacy or no gamblers fallacy, I'm betting on "girl".
A coin is flipped 9 times and comes up "heads" each time. What is
the probability that the coin is not a fair coin?
TwoBirds
It showed a confident-looking tv weather-announcer saying
"...and for tomorrow there is a 10% chance of snow...".
The caption said "And what are our chances that the weather
announcer knows what he's talking about."
Matthew T. Russotto wrote in message
<6Wgw2.439$ip.7...@newshog.newsread.com>...