Challenge your brains! Can you solve this problem?

[Bahku]

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?

Algebraically, the answer has to be 1 in 3.

Can you show your work? 

My thought was the same as Fan from VT's; the gender of the second dog has nothing to do with the gender of the male dog (i.e., it's an independent event).  Thus, it can be male or female, so it's 50/50, right?

Exactly what I thought. It's an independent event so it should be 50%

Say you were picking them randomly, these would be the variables:

Female/Female
Female/Male
Male/Female
Male/Male ...

with the info gievn you are eliminating the last: Male/Male (because the probability being decided, it's 100% Male) ...

 ... you are then left with:

Female/Female
Female/Male
Male/Female

.. this leaves a 1 in 3 chance of the determining the other sex.

Why do you eliminate the Male/Male option? 

Say you could flip the puppies like coins, each time you flip them, you have the four variables I listed, by the info given, the Male/Male variable is eliminated, because it's already determined ... that leaves three variables, and a one in three chance of determining the outcome.

[GKC]

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?

Algebraically, the answer has to be 1 in 3.

Can you show your work? 

My thought was the same as Fan from VT's; the gender of the second dog has nothing to do with the gender of the male dog (i.e., it's an independent event).  Thus, it can be male or female, so it's 50/50, right?

Exactly what I thought. It's an independent event so it should be 50%

Say you were picking them randomly, these would be the variables:

Female/Female
Female/Male
Male/Female
Male/Male ...

with the info gievn you are eliminating the last: Male/Male (because the probability being decided, it's 100% Male) ...

 ... you are then left with:

Female/Female
Female/Male
Male/Female

.. this leaves a 1 in 3 chance of the determining the other sex.

I think you meant eliminating Female/Female.

[GKC]

1 in 3 is correct.

The question is not flipping a coin one after the other. It is flipping 2 coins at the same time.

The out comes are

Heads / Tails
Heads / Heads
Tails / Tails
Tails / Heads

The question is, if I told you one of them was heads, what are the odds the other one is heads?

Obviously Tails / Tails is eliminated.

So it's 1 in 3. My previous answer of 50% was wrong.

Great question.

[Bahku]

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?

Algebraically, the answer has to be 1 in 3.

Can you show your work? 

My thought was the same as Fan from VT's; the gender of the second dog has nothing to do with the gender of the male dog (i.e., it's an independent event).  Thus, it can be male or female, so it's 50/50, right?

Exactly what I thought. It's an independent event so it should be 50%

Say you were picking them randomly, these would be the variables:

Female/Female
Female/Male
Male/Female
Male/Male ...

with the info gievn you are eliminating the last: Male/Male (because the probability being decided, it's 100% Male) ...

 ... you are then left with:

Female/Female
Female/Male
Male/Female

.. this leaves a 1 in 3 chance of the determining the other sex.

The question says "what are the odds that the other one is male?"  I.e., what are the chances that the dog you don't know the gender of is male?

In other words, Dog #1 = male.  Thus, you only have two other outcomes:  male or female.  Thus, it's 50%.

No ... only if you're considering the sex of one ... this male/female paradox has been studied and investigated extensively, and the answer depends completely on how the information is given. In this case, the info is presented with two variables: Male and Male, thus eliminating the first option of 4 variants. It leaves three ... and the answer is 1/3.

We are only considering the sex of one:  "the other one".  We don't know which dog is the one that is definitely male, but we don't have to.  We just need to know the gender of the "other" one.  The "other" one can only be one of two genders.

ok

[Roy Hobbs]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

[Bahku]

1 in 3 is correct.

The question is not flipping a coin one after the other. It is flipping 2 coins at the same time.

The out comes are

Heads / Tails
Heads / Heads
Tails / Tails
Tails / Heads

The question is, if I told you one of them was heads, what are the odds the other one is heads?

Obviously Tails / Tails is eliminated.

So it's 1 in 3. My previous answer of 50% was wrong.

Great question.

Thank you ... I wasn't sure exactly how else to show it.

[Bahku]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

[bdm860]

I think we should ban Bahku, he's flipping puppies!  Don't go easy on him cuz he's one of us, treat him like Michael Vick!  Where's the report to a mod button 

http://www.youtube.com/watch?v=_AoSmv8skaY

[Roy Hobbs]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

[Bahku]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

This is a statistical probelm, so the answer has to be statistical, (whatever the internet says), and it has to be 1 in 3. I'm out on this one ... my brain longs for mindless television.

[mgent]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

You're correct, but they want the probability.
There's 3 options:

Male/Female
Female/Male
Male/Male

Each is a 1/3 probability.  But they don't tell you which one is male, so both of the first two are possible.


If the second dog is female, it could be EITHER:

Male/Female
OR
Female/Male

So the probability of the second dog being a female is 2/3.



It's weird, because it's a paradox.
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

[Roy Hobbs]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

You're correct, but they want the probability.
There's 3 options:

Male/Female
Female/Male
Male/Male

Each is a 1/3 probability.  But they don't tell you which one is male, so both of the first two are possible.


If the second dog is female, it could be EITHER:

Male/Female
OR
Female/Male

So the probability of the second dog being a female is 2/3.



It's weird, because it's a paradox.
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

I think it's in the wording.

If the question is "What are the chances that both dogs are male?", it's 1/3.

If the question is "What are the chances that the *other* dog (i.e., the one that could be male or female) is male?", it's 1/2.

You *know* dog #1 is male.  It can't be female, because you're only asked to look for the "other".  Therefore, "female/male" isn't an option (nor, of course, is "female/female".  You're left with either "male/male", or "male/female".

If the answer that was sought was 1/3, the question should have been posed correctly.  The "other" can only be male or female; it can't be a third gender.

[guava_wrench]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

This is a statistical probelm, so the answer has to be statistical, (whatever the internet says), and it has to be 1 in 3. I'm out on this one ... my brain longs for mindless television.

This sounds like a wannabe Monty Hall problem.

With 2 dogs,

There is 1/4 chance of 2 males
a 1/4 chance of 2 females
a 1/2 chance of one of each

By knowing the gender of one dog, you can eliminate one of the 1/4 outcomes from the analysis, leaving the 1/3 answer.

[Bahku]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

This is a statistical probelm, so the answer has to be statistical, (whatever the internet says), and it has to be 1 in 3. I'm out on this one ... my brain longs for mindless television.

This sounds like a wannabe Monty Hall problem.

With 2 dogs,

There is 1/4 chance of 2 males
a 1/4 chance of 2 females
a 1/2 chance of one of each

By knowing the gender of one dog, you can eliminate one of the 1/4 outcomes from the analysis, leaving the 1/3 answer.

Yes. (TP) But the paradox does depend on how the info is presented, and in this one, the answer has to be 1 in 3.

[mgent]

I agree there are three possibilities for the dogs:

Male/Female
Female/Male
Male/Male

However, we're asked to determine the gender of the *other* dog.  Thus, we have to accept that dog #1 is male (we just don't know which one is dog #1).  Thus, we're asked to determine the gender of dog #2 (without knowing which dog is dog #2).  Dog #2 can only be male or female, thus 50/50.

Statistics don't work that way, you still have to factor in the original variable ... just because it's supplied already, doesn't negate it's value to the problem.

Statistics don't give the right answer here.  The second dog can only be one of two genders.  There's no third gender, so it's got to be 50/50.

Maybe the traditional puzzle found on the internet provides a different answer, but the way this one was worded (i.e., what's the gender of "the other one") means it's 50/50.

You're correct, but they want the probability.
There's 3 options:

Male/Female
Female/Male
Male/Male

Each is a 1/3 probability.  But they don't tell you which one is male, so both of the first two are possible.


If the second dog is female, it could be EITHER:

Male/Female
OR
Female/Male

So the probability of the second dog being a female is 2/3.



It's weird, because it's a paradox.
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

I think it's in the wording.

If the question is "What are the chances that both dogs are male?", it's 1/3.

If the question is "What are the chances that the *other* dog (i.e., the one that could be male or female) is male?", it's 1/2.

You *know* dog #1 is male.  It can't be female, because you're only asked to look for the "other".  Therefore, "female/male" isn't an option (nor, of course, is "female/female".  You're left with either "male/male", or "male/female".

If the answer that was sought was 1/3, the question should have been posed correctly.  The "other" can only be male or female; it can't be a third gender.

There isn't a third gender.
There's a 1/3 probability that it's a male and a 2/3 probability that it's a female.

Think about it like this:

Female/Female 1/4
Male/Female 1/4
Female/Male 1/4
Male/Male 1/4

So the probability that one dog is male and the other is female is 1/2.  They don't tell you which dog is the male.

There's twice the chance the dogs are a pair than both male.