Challenge your brains! Can you solve this problem?

[nickagneta]

This is a very easy answer because of the use of the word "other". In the flawed thinking of the 1/3 answer what you people are leaving out is that you already now that one specific dog(Dog1) is guaranteed to be male.


Dog1/Dog2
Female/Female
Female/Male
Male/Female
Male/Male

So Female/Female is eliminated because because both can't be female. That leaves three options.

Dog1/Dog2
Female/Male
Male/Female
Male/Male

But because Dog1 is guaranteed to be a male you also have to eliminate the Female/Male option. That leaves:

Male/Female
Male/Male

It is all keyed by the use of the word other in the word problem which automatically designates Dog1 as male. That's where most mathematicians and statistically oriented people get fooled. This is not a math or statistics problem. The use of the word "other" makes this a logic problem and logically speaking there is only one of two sexes the "other" dog can be.

Answer is easily 50%

But you don't know WHICH dog is the male.

Yes, you do. One dog is male, what is the "other". It is pure logic. This is not a statistical problem. Typically in these trick questions it is the wording that determines the answer and in this question it is clearly that one dog is male what is the "other". It is not one of the dogs is male what is the chances of both being male. That is not the question but what they try to do is trick the mathematically inclined mind into thinking this is a statistics question. It isn't. It's logic.

[GKC]

This is a very easy answer because of the use of the word "other". In the flawed thinking of the 1/3 answer what you people are leaving out is that you already now that one specific dog(Dog1) is guaranteed to be male.


Dog1/Dog2
Female/Female
Female/Male
Male/Female
Male/Male

So Female/Female is eliminated because because both can't be female. That leaves three options.

Dog1/Dog2
Female/Male
Male/Female
Male/Male

But because Dog1 is guaranteed to be a male you also have to eliminate the Female/Male option. That leaves:

Male/Female
Male/Male

It is all keyed by the use of the word other in the word problem which automatically designates Dog1 as male. That's where most mathematicians and statistically oriented people get fooled. This is not a math or statistics problem. The use of the word "other" makes this a logic problem and logically speaking there is only one of two sexes the "other" dog can be.

Answer is easily 50%

But you don't know WHICH dog is the male.

Yes, you do. One dog is male, what is the "other". It is pure logic. This is not a statistical problem. Typically in these trick questions it is the wording that determines the answer and in this question it is clearly that one dog is male what is the "other". It is not one of the dogs is male what is the chances of both being male. That is not the question but what they try to do is trick the mathematically inclined mind into thinking this is a statistics question. It isn't. It's logic.

We're arguing the wording of the problem. At this point it doesn't matter.

[Roy Hobbs]

And of course, if you want to get philosophical, the answer is either 0% or 100%.  If the dog is, in fact, male, there's a 100% chance it's a male dog, and if it's female, there's a 0% chance.

[Bahku]

And of course, if you want to get philosophical, the answer is either 0% or 100%.  If the dog is, in fact, male, there's a 100% chance it's a male dog, and if it's female, there's a 0% chance.

I like that ... we have a winner!

[mgent]

Let me attempt another example:

Say there are two sets of parents (couple A and couple B) and each have 2 children.
At least one of couple A's children is male.
Couple B's oldest child is male.
The question is "What's the probability that both children are male for each couple?"

The answers are:
Couple A, 1/3
Couple B, 1/2


Couple A has 3 possibilities:
2 boys
an older boy and a younger girl
an older girl and a younger boy

Couple B only has 2 possibilities:
2 boys
an older boy and a younger girl

Couple B can't have an older girl and a younger boy, and neither couples can have 2 girls.

Couple A is the same thing as the dog question.
In Couple B, it is specifically stated which child is the boy (the elder child), whereas with the dogs you had no clue which dog was male (the first dog or the second dog).  Because there are two variables (two dogs and two genders) the probability is different than if there was only one variable as seen in Couple B where there was two genders, but you were only dealing with one child (the younger one).


I hope this clears things up.

[nickagneta]

Let me attempt another example:

Say there are two sets of parents (couple A and couple B) and each have 2 children.
At least one of couple A's children is male.
Couple B's oldest child is male.
The question is "What's the probability that both children are male for each couple?"

The answers are:
Couple A, 1/3
Couple B, 1/2


Couple A has 3 possibilities:
2 boys
an older boy and a younger girl
an older girl and a younger boy

Couple B only has 2 possibilities:
2 boys
an older boy and a younger girl

Couple B can't have an older girl and a younger boy, and neither couples can have 2 girls.

Couple A is the same thing as the dog question.
In Couple B, it is specifically stated which child is the boy (the elder child), whereas with the dogs you had no clue which dog was male (the first dog or the second dog).  Because there are two variables (two dogs and two genders) the probability is different than if there was only one variable as seen in Couple B where there was two genders, but you were only dealing with one child (the younger one).


I hope this clears things up.

Again, you are imposing more variables into the question than actually exist or are asked for. This is a very simple logic question rapped into a statistical camouflage because of the word "probability". It is a trick question due to the use of the word "other" which automatically designates one dog as male and now you have to find out the "other" dog's sex.

If the question was worded differently, you are in fact, correct. I once had to take a logic/math test as a hiring practice for this company I applied for. I did outstanding because in these word problems you have to read the question carefully and try to understand whether they are asking a logic problem or a math problem.

This problem, due to the use of the word "other" is clearly a logic problem. It's no wonder Roy had the correct answer because lawyers, at least really good ones, tend to have to interpret the exact meaning of the written word in documents every day. They should on most occassions be able to pick apart these type of word problems.

[KJR]

yes, Nick and Roy are correct

it all depends on the wording of the question

there is no reason to introduce additional variables into the answer that were not stated as part of the question

why specify the ages of the children?  why not hair color, height, shoe size etc.  you're just adding random variables; in theory, the answer is 1 in an infinite number: male with blonde hair, female with red shoes, etc.

if you ask a general question, you'll get a general answer, and the answer in the original example is always 50%

if you want to get a 1 in 3, or a 2 in 3 result, you need to ask a different question: if at least one of the children is male, what are the odds that the older child is male (2 in 3) and what are the odds that the older child is female (1 in 3), etc.

[mgent]

Let me attempt another example:

Say there are two sets of parents (couple A and couple B) and each have 2 children.
At least one of couple A's children is male.
Couple B's oldest child is male.
The question is "What's the probability that both children are male for each couple?"

The answers are:
Couple A, 1/3
Couple B, 1/2


Couple A has 3 possibilities:
2 boys
an older boy and a younger girl
an older girl and a younger boy

Couple B only has 2 possibilities:
2 boys
an older boy and a younger girl

Couple B can't have an older girl and a younger boy, and neither couples can have 2 girls.

Couple A is the same thing as the dog question.
In Couple B, it is specifically stated which child is the boy (the elder child), whereas with the dogs you had no clue which dog was male (the first dog or the second dog).  Because there are two variables (two dogs and two genders) the probability is different than if there was only one variable as seen in Couple B where there was two genders, but you were only dealing with one child (the younger one).


I hope this clears things up.

Again, you are imposing more variables into the question than actually exist or are asked for. This is a very simple logic question rapped into a statistical camouflage because of the word "probability". It is a trick question due to the use of the word "other" which automatically designates one dog as male and now you have to find out the "other" dog's sex.

If the question was worded differently, you are in fact, correct. I once had to take a logic/math test as a hiring practice for this company I applied for. I did outstanding because in these word problems you have to read the question carefully and try to understand whether they are asking a logic problem or a math problem.

This problem, due to the use of the word "other" is clearly a logic problem. It's no wonder Roy had the correct answer because lawyers, at least really good ones, tend to have to interpret the exact meaning of the written word in documents every day. They should on most occassions be able to pick apart these type of word problems.

It's not a trick question, and I promise you the wording is not meant to trick you.  It's not a statistical problem either.  It's simply a mind game where you have to look beyond the initial question.  You're oversimplifying it.  It's meant to look illogical because the question is based on a paradox.

You're giving the intuitive answer, but the probabilities in the dog question are CONDITIONAL, not absolute.

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

[nickagneta]

Let me attempt another example:

Say there are two sets of parents (couple A and couple B) and each have 2 children.
At least one of couple A's children is male.
Couple B's oldest child is male.
The question is "What's the probability that both children are male for each couple?"

The answers are:
Couple A, 1/3
Couple B, 1/2


Couple A has 3 possibilities:
2 boys
an older boy and a younger girl
an older girl and a younger boy

Couple B only has 2 possibilities:
2 boys
an older boy and a younger girl

Couple B can't have an older girl and a younger boy, and neither couples can have 2 girls.

Couple A is the same thing as the dog question.
In Couple B, it is specifically stated which child is the boy (the elder child), whereas with the dogs you had no clue which dog was male (the first dog or the second dog).  Because there are two variables (two dogs and two genders) the probability is different than if there was only one variable as seen in Couple B where there was two genders, but you were only dealing with one child (the younger one).


I hope this clears things up.

Again, you are imposing more variables into the question than actually exist or are asked for. This is a very simple logic question rapped into a statistical camouflage because of the word "probability". It is a trick question due to the use of the word "other" which automatically designates one dog as male and now you have to find out the "other" dog's sex.

If the question was worded differently, you are in fact, correct. I once had to take a logic/math test as a hiring practice for this company I applied for. I did outstanding because in these word problems you have to read the question carefully and try to understand whether they are asking a logic problem or a math problem.

This problem, due to the use of the word "other" is clearly a logic problem. It's no wonder Roy had the correct answer because lawyers, at least really good ones, tend to have to interpret the exact meaning of the written word in documents every day. They should on most occassions be able to pick apart these type of word problems.

It's not a trick question, and I promise you the wording is not meant to trick you.  It's not a statistical problem either.  It's simply a mind game where you have to look beyond the initial question.  You're oversimplifying it.  It's meant to look illogical because the question is based on a paradox.

You're giving the intuitive answer, but the probabilities in the dog question are CONDITIONAL, not absolute.

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

This is not the two child question. Check out the wording of the two child question from your wiki reference:

    * Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?"
    * Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?

These are two different questions which you are being tricked into thinking they are the same. They are not. The two child question is asking for the probability of two children being one thing. Your question is asking for the probability of the "other" dog not the combined entity of the chances of both dogs being the same thing. Two completely different questions. If that was the question, you are clearly correct but the wording throws out that possibility.

[mgent]

Let me attempt another example:

Say there are two sets of parents (couple A and couple B) and each have 2 children.
At least one of couple A's children is male.
Couple B's oldest child is male.
The question is "What's the probability that both children are male for each couple?"

The answers are:
Couple A, 1/3
Couple B, 1/2


Couple A has 3 possibilities:
2 boys
an older boy and a younger girl
an older girl and a younger boy

Couple B only has 2 possibilities:
2 boys
an older boy and a younger girl

Couple B can't have an older girl and a younger boy, and neither couples can have 2 girls.

Couple A is the same thing as the dog question.
In Couple B, it is specifically stated which child is the boy (the elder child), whereas with the dogs you had no clue which dog was male (the first dog or the second dog).  Because there are two variables (two dogs and two genders) the probability is different than if there was only one variable as seen in Couple B where there was two genders, but you were only dealing with one child (the younger one).


I hope this clears things up.

Again, you are imposing more variables into the question than actually exist or are asked for. This is a very simple logic question rapped into a statistical camouflage because of the word "probability". It is a trick question due to the use of the word "other" which automatically designates one dog as male and now you have to find out the "other" dog's sex.

If the question was worded differently, you are in fact, correct. I once had to take a logic/math test as a hiring practice for this company I applied for. I did outstanding because in these word problems you have to read the question carefully and try to understand whether they are asking a logic problem or a math problem.

This problem, due to the use of the word "other" is clearly a logic problem. It's no wonder Roy had the correct answer because lawyers, at least really good ones, tend to have to interpret the exact meaning of the written word in documents every day. They should on most occassions be able to pick apart these type of word problems.

It's not a trick question, and I promise you the wording is not meant to trick you.  It's not a statistical problem either.  It's simply a mind game where you have to look beyond the initial question.  You're oversimplifying it.  It's meant to look illogical because the question is based on a paradox.

You're giving the intuitive answer, but the probabilities in the dog question are CONDITIONAL, not absolute.

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

This is not the two child question. Check out the wording of the two child question from your wiki reference:

    * Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?"
    * Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?

These are two different questions which you are being tricked into thinking they are the same. They are not. The two child question is asking for the probability of two children being one thing. Your question is asking for the probability of the "other" dog not the combined entity of the chances of both dogs being the same thing. Two completely different questions. If that was the question, you are clearly correct but the wording throws out that possibility.

In a post I related the two questions.  The dog question is the same as the Mr. Smith question.

Neither dog was specified as being male, as is the case with Mr. Jones.  If you go back to my post I tried to relate the two problems a little better.

The dog question said at least one was male.  This doesn't mean you can pick which dog is male.  The word "other" doesn't specify which dog is which gender either.

[Bahku]

I spent about 3 consecutive "Statistics" classes in college, (around 6 hours), with 20 others, discussing a very similar problem/puzzle, with the same presentation and variables, and the paradoxes just keep changing, dependent completely on where you start the process, what info is presented initially, how you interpret the phrasing of the question, and so on ... it's really a question without a clearly defined answer, because each option presented here by each of us, is dependent on how we interpret the data and how it's presented, and we're all basically deciding how we accept how the question is asked, in order to make it fit the answer we feel is correct. There will never be one clear solution to this problem, because one doesn't exist ... but it really is great to bang this stuff around, cuz it gets the gears turning, (which are a bit rusty in my case).

[mgent]

I spent about 3 consecutive "Statistics" classes in college, (around 6 hours), with 20 others, discussing a very similar problem/puzzle, with the same presentation and variables, and the paradoxes just keep changing, dependent completely on where you start the process, what info is presented initially, how you interpret the phrasing of the question, and so on ... it's really a question without a clearly defined answer, because each option presented here by each of us, is dependent on how we interpret the data and how it's presented, and we're all basically deciding how we accept how the question is asked, in order to make it fit the answer we feel is correct. There will never be one clear solution to this problem, because one doesn't exist ... but it really is great to bang this stuff around, cuz it gets the gears turning, (which are a bit rusty in my case).

But the question can only be asking one thing.  Just because someone interprets it wrong, it doesn't mean there's suddenly two answers.

[Fafnir]

Your question is asking for the probability of the "other" dog not the combined entity of the chances of both dogs being the same thing. Two completely different questions. If that was the question, you are clearly correct but the wording throws out that possibility.

Nick you're wrong on what the wording says. It clearly is asking if both dogs are male. One arbitrary dog is given a gender, male. The other is unspecified, the only case in which it can be male both dogs must be male.

Conditional probability formula.

Things get confusing with it. Another famous example the "Monty Hall Problem".

The Monty Hall thing doesn't make much sense either, but its true. We actually ran a in person Monte Carlo simulation for are class once just to prove the result. I just kept mixing up flash cards and having a classmate pick a card.

[Bahku]

I spent about 3 consecutive "Statistics" classes in college, (around 6 hours), with 20 others, discussing a very similar problem/puzzle, with the same presentation and variables, and the paradoxes just keep changing, dependent completely on where you start the process, what info is presented initially, how you interpret the phrasing of the question, and so on ... it's really a question without a clearly defined answer, because each option presented here by each of us, is dependent on how we interpret the data and how it's presented, and we're all basically deciding how we accept how the question is asked, in order to make it fit the answer we feel is correct. There will never be one clear solution to this problem, because one doesn't exist ... but it really is great to bang this stuff around, cuz it gets the gears turning, (which are a bit rusty in my case).

But the question can only be asking one thing.  Just because someone interprets it wrong, it doesn't mean there's suddenly two answers.

But it's not being interpreted wrong, it's being interpreted differently. It's similar to me giving you three coins ... you can say that I gave you three coins, or that you had no coins and then you had three, or that I had three coins and gave them all to you, or that I gave you three coins, one at a time, or that you took three coins from me. With a puzzle like this, the answer is going to depend on how you interpret the info given, and none of these is incorrect. But when making assumptions about the result, how it's presented affects how you get to the conclusion. (I'll leave it to you guys ... the ol' eyelids are drooping.) This was fun ... kind of.

[Fafnir]

I spent about 3 consecutive "Statistics" classes in college, (around 6 hours), with 20 others, discussing a very similar problem/puzzle, with the same presentation and variables, and the paradoxes just keep changing, dependent completely on where you start the process, what info is presented initially, how you interpret the phrasing of the question, and so on ... it's really a question without a clearly defined answer, because each option presented here by each of us, is dependent on how we interpret the data and how it's presented, and we're all basically deciding how we accept how the question is asked, in order to make it fit the answer we feel is correct. There will never be one clear solution to this problem, because one doesn't exist ... but it really is great to bang this stuff around, cuz it gets the gears turning, (which are a bit rusty in my case).

But the question can only be asking one thing.  Just because someone interprets it wrong, it doesn't mean there's suddenly two answers.

Yes and no, read the Monty Hall link. You have to be very specific with these sort of problems. The simple formulation of word puzzles often leads to no rigorous solution.