Quick Logic Problem

wait a second you are right there are 6 possible outcomes. It is stipulated that Joans oldest child is a boy where as with jane either the oldest or the youngest can be a boy. That gives us 6 possible outcomes. Joan can have two out comes. BB and BG. Jane can have 3 outcomes BB, BG and GB. That gives us these possibilities or

Joan X Jane
BB BB
BG BG
GB
or

BBBB
BBBG
BBGB
BGBB
BGBG
BGGB

Total possibilities are 6

Since we are calculating 1 simple outcome (BBBB) with 6 possibilities the probability of a 4 children being boys, under the coniditions stated, would be 1 in 6 or 16.7%
 
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tinfoil said:
Would you mind teaching an old dog an old trick he forgot? LOL

is that 25% + 25%*25%
I knew I was close.

I multiplied when I shoulda added the square.

Can you please run quickly throught the math?
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Na, I jumped the gun and figured the wrong # of possible outcomes. I was wrong on my first attempt. The correct answer is 16.7%.
 
Mottleydude said:
Na, I jumped the gun and figured the wrong # of possible outcomes. I was wrong on my first attempt. The correct answer is 16.7%.
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Wrong.... it is 25%. The fact that we don't know whether the boy is the youngest or oldest does not matter. We know one of the two is fixed. That means the remaining child has a 50/50 chance of being a boy.
 
Superfreak said:
again, show me the actual survey questions and results, then we can discuss her survey.

The laws of probability do NOT support the results.
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What questions? She asked her readers who had 2 kids with at least one of them being a boy to say what the 2 kids they had were and the results are below:

"Finally vos Savant started a survey, calling on women readers with exactly two children and at least one boy to tell her the sex of both children. With almost eighteen thousand responses, the results showed 35.9% (a little over 1 in 3) with two boys"

The laws of probability are exactly what support the results, for crying out loud you wrote them yourself when you got the answer to this problem right. There are 3 possible combinations of 2 kids for Jane with one of them having to be a boy, thus a 1 in 3 probability.

Dano, the smartest woman in the world, the algebra teacher in the story and the survey of 18000 people are not all wrong.
 
Superfreak said:
Wrong.... it is 25%. The fact that we don't know whether the boy is the youngest or oldest does not matter. We know one of the two is fixed. That means the remaining child has a 50/50 chance of being a boy.
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No you're wrong, you know if it makes you feel better, I jumped to the same conclusion you did before I realized. But that was the whole nature of the questions this lady gets. Basically she writes a column where people try and give challenging problems for her to solve, the simplest answer is rarely going to be the correct one or it would be a pretty boring column.
 
Superfreak said:
Wrong.... it is 25%. The fact that we don't know whether the boy is the youngest or oldest does not matter. We know one of the two is fixed. That means the remaining child has a 50/50 chance of being a boy.
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Nope, the correct answer is 1/6.
 
KingCondanomation said:
People vary in ethnicity by geography, but the ratio of boys to girls by geography largely does not.
I would find far more Chinese people in California than Tennessee, but I would still see roughly the same ratio of boys/girls in Cali that I see in Tennessee.
The people in the survey are the readers of her column, they LIKELY have a higher IQ average than the norm, but there is no bias reason whatsoever they would have children where more would be skewed to having a boy and a girl instead of 2 boys.
They do so because the probability was higher.
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It doesn't matter how you try to play it, you are simply wrong on the math.

The survey was not valid because they sought out specific scenarios rather than the one salient fact, one child was male. It doesn't matter which order they were born in. Because they sought a specific number with the "first child male" and then added in "second child male" they simply outwitted themselves.

Using poor logic and creating such a "survey" you will mess up your own results. It is not salient to the math when the one "boy" was born.

Again. If you name the boy, you wind up with four possible scenarios.

John - Girl
John - Boy
Boy - John
Girl - John

Each with a 25% probability, However with only two results one boy and one girl or two boys.

This creates an exact 50% probability the child of the unknown sex was a boy.

In the other scenario where we know the boy was born first you get only two.

John - Girl
John - Boy

Still 50%.

You take the two variables and multiply their probability, and you get the result of the full probability you want.

Ask any statistics teacher, you will get the same result.

Bad math doesn't make what you say true, because it simply isn't.
 
Tomorrow, I'm going to post some actual Logical and Analytical Reasoning problems from the LSAT and it will be interesting to see how ppl do on them.
 
I had forgoten how much I love puzzles until I had to brush up for the LSAT.

Some of those analytical reasoning problems just tear your brain apart though. It's too much information to be able to hold in your head and work from. I'll show you this one but I'll put up a better one tomorrow:
 
I.

A particular seafood restaurant serves dinner Tuesday through Sunday. The restaurant is closed on Monday. Five entrees—snapper, halibut, lobster, mahi mahi, and tuna—are served each week according to the following restrictions:


Givens:
Halibut is served on three days each week, but never on Friday.

Lobster is served on one day each week.

Mahi mahi is served on three days each week, but never on consecutive days.

Halibut and snapper are both served on Saturday and Sunday.

Tuna is served five days each week.

No more than three different entrees are served on any given day.

Question One:
On which of the following pairs of days could the restaurant's menu of entrees be identical?

(A) Friday and Sunday
(B) Tuesday and Wednesday
(C) Saturday and Sunday
(D) Wednesday and Friday
(E) Thursday and Friday

Question 2
Which of the following is a complete and accurate list of the days on which halibut and lobster may both be served?

(A) Tuesday, Thursday
(B) Tuesday, Wednesday, Thursday
(C) Monday, Tuesday, Wednesday
(D) Tuesday, Wednesday, Thursday, Friday
(E) Tuesday, Wednesday, Thursday, Saturday

Question Three
If mahi mahi is served on Saturday, it could be true that

(A) snapper and mahi mahi are both served on Sunday
(B) snapper and halibut are both served on Tuesday
(C) lobster and halibut are both served on Thursday
(D) tuna and snapper are both served on Saturday
(E) lobster and snapper are both served on Friday

Question Four
Which of the following statements provides sufficient information to determine on which three days halibut is served?

(A) Mahi mahi and lobster are served on the same
...........day.
(B) Lobster and snapper are both served on
...........Tuesday.
(C) Tuna is served on Saturday, and lobster is served
...........on Tuesday.
(D) Mahi mahi is served on Saturday, and snapper is
...........served on all but one of the six days.
(E) Tuna is served on Sunday, and snapper is served
...........on Tuesday and Thursday.
 
Damocles said:
It doesn't matter how you try to play it, you are simply wrong on the math.

The survey was not valid because they sought out specific scenarios rather than the one salient fact, one child was male.
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That is false, she specifically asked for "Jane's" to respond, that is people who have 2 children where one is male.

Damocles said:
It doesn't matter which order they were born in. Because they sought a specific number with the "first child male" and then added in "second child male" they simply outwitted themselves.

Using poor logic and creating such a "survey" you will mess up your own results. It is not salient to the math when the one "boy" was born.

Again. If you name the boy, you wind up with four possible scenarios.

John - Girl
John - Boy
Boy - John
Girl - John

Each with a 25% probability, However with only two results one boy and one girl or two boys.

This creates an exact 50% probability the child of the unknown sex was a boy.

In the other scenario where we know the boy was born first you get only two.

John - Girl
John - Boy

Still 50%.

You take the two variables and multiply their probability, and you get the result of the full probability you want.

Ask any statistics teacher, you will get the same result.

Bad math doesn't make what you say true, because it simply isn't.
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I don't know how else I can explain this.
Damo, there are people in the world who have 2 kids and the 1st is male, there are probably roughly the same amount of people in the world who have 2 kids where the 2nd is male. Do you agree with that?
If you were to ask for all those who have at least one male as the first OR at least one male as the second, you are going to get a larger group (roughly double the size) than just asking for those who have male only for both.

It's not Dano, the algebra teacher in the story, the smartest woman in the world and a massive survey results of 18000 people that are wrong. Think about how much of a stretch that is, the survey is completely valid as it asks for people EXACTLY like Jane and from a sample that is not bias in any fashion to answering facts that they cannot be bias on (ie: which kids they have).
 
Just reading through the thread it has become very clear to me why the Chinese State introduced their "one child" policy.
 
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