Poll: A little math problem

[thedoclc]

Surprising how much food a troll got here...

I'll try to explain the solution to this problem.

We start with no knowledge of the dogs' gender. I'll name the dogs: Sparky and Spot.

So before we call, we have four possibilities for the dogs' gender. All are equally probably.
1 in 4: Sparky Male, Spot Male
1 in 4: Sparky Male, Spot Female
1 in 4: Sparky Female, Spot Male
1 in 4: Sparky Female, Spot Female

These probabilities add up to one, representing all possible combinations.

Now the shopkeeper makes the phone call. We eliminate the Female/Female pairing, so that means we now have only three equally probably situations. In all three cases that remain, the statement "at least one dog is male" is true. We also have no reason to assume that any of the possibilities is more likely than any of the others. We have to adjust our probabilities to add up to 1, since the sum of the probabilities of all possible outcomes equals 1. That 1 in 4 initially given to Sparky and Spot both being female is divided into the three remaining equally likely possibilities.

So before we make the adjustment, we're at:
1 in X: Sparky Male, Spot Male
1 in X: Sparky Male, Spot Female
1 in X: Sparky Female, Spot Male
0: Sparky Female, Spot Female

Dividing 1/4 by 3, we get 1/12. 1/4 + 1/12 = 4/12, or 1/3.

The assumptions in the problem are that male and female are equally likely (not true), the chances of some oddball offspring are zero, and that the fellow bathing the dogs is an idiot who only answers the question literally and doesn't think to say, "Oh, yeah, one is, but the other is a girl," or "Both are."

 

[Blind Punk Riot]

Yes you do.

One is male, it doesnt matter if that is dog 2 or dog 1.

And also hypocrisy?
This is opinion this is fact.


And the fact is; you are wrong.



You only have two dogs. One is male. There is one dog left to guess the sex of.

Ok?
So what is the odds. Please, Please, Please understand.

And thank god "cleverlymadeup" and many others can understand.



But I think I'll still go ahead and start looking in the universe's personals for different species to join.

 

[Blind Punk Riot]

I'm sorry, but if any of you go to school still, or college, or university.

Please ask your teacher/tutor this question.

Write the question down word for word and show them it.
They will say 50% and laugh at you, depending on how mean they are.

 

[thedoclc]

I'm sorry, but if any of you go to school still, or college, or university.

Please ask your teacher/tutor this question.

Write the question down word for word and show them it.
They will say 50% and laugh at you, depending on how mean they are.

And they would be wrong.

Or not, since most of mine are geneticists or biochemists quite used to working out the probabilities of inheritance and demanding we do the same.

 

[TKTom]

I'm sorry, but if any of you go to school still, or college, or university.

Please ask your teacher/tutor this question.

Write the question down word for word and show them it.
They will say 50% and laugh at you, depending on how mean they are.

They would laugh at me, but only for bringing them such a simple question.

The sample space has already been said : M/M, M/F, F/M, F/F

Now the events must be sorted correctly; m1: the event that one dog is male.
m2: The event that the other dog is male.

You are told that m1 has occured, therefore the probabilty you want is

P(m2 | m1)= P(m2&m1)/P(m1)=0.25/0.75=1/3

The only way m2&m1 occur is the M/M outcome, which has the probability of 0.25. The ways that m1 occur alone are M/M, M/F, F/M, meaning it has a probabiliy of 0.75.

 

[Ancalagon]

Dog 1 male - from the problem, at least one is male, so this one will always be male, if you move it to dog 2 it doesn't change

That's exactly where the problem comes from. You're assuming that you can call dog A male, since in the situation 'dog A is female, dog B is male', you can just swap the dogs around. Well you can, but you've altered the probability that dog B is male. Because one third of the time dog A was male, and dog B was female. Another third of the time, dog A was female, and dog B was male, but you swapped them, so dog B is now female. The last third, they were both male. So the probability that the other dog was male is 33%.

 

[Blind Punk Riot]

They would laugh at me, but only for bringing them such a simple question.

The sample space has already been said : M/M, M/F, F/M, F/F

Now the events must be sorted correctly; m1: the event that one dog is male.
m2: The event that the other dog is male.

You are told that m1 has occured, therefore the probabilty you want is

P(m2 | m1)= P(m2&m1)/P(m1)=0.25/0.75

And you would be correct.
If you weren't told that one of them is male to begin with.

ONE OF THEM IS MALE.

Therefore you only have the probablity of the other one.


One is male, therefore you discount the odds of that one.
Thats what you do.



Go to them and tell them what you just said aswell
they will seriously lolololololol

 

[irrelevantnugget]

I'm sorry, but if any of you go to school still, or college, or university.

Please ask your teacher/tutor this question.

Write the question down word for word and show them it.
They will say 50% and laugh at you, depending on how mean they are.

And they would be wrong.

Seriously, Riot.
How can you just say that everybody should be entitled to his/her own opinions, then blatantly say that everybody NOT saying 50% is wrong?

Also, WE HAVE EXPLAINED IT.
READ IT. TRY TO UNDERSTAND IT.

This will be my last post in here, because some people simply can't think for themselves and go with the mob, and this is simply infuriating me.

Just ADMIT that you're wrong for a change, there's NOTHING wrong with that.

Am I being a hypocrite now? No. This is math, not ethics. Math is an exact science: this means that there is one answer, and ONLY one, if you're asking a simple question, at least. 1+1 is not either 2 or 3, it clearly is 2.

I understand the matter of this question, I understand the answer, and professors have calculated this and say this is a fact.

SO.

2 dogs. 4 possibilities:
1) A is male, B is female
2) A is female, B is male
3) A is male, B is male
4) A is female, B is female.

Shopkeeper says that 1 dog is male.
What most people do at this point, is assign the 'male' attribute to Dog A automatically, taking only options 1 and 3 for their 1/2 solution. (That includes you)
It is however, never said that Dog A is that male. The option that Dog A is female, and Dog B was the male the shopkeeper talked about, still exists and should NOT be discarded.

So the only real option that is tossed out the window, is option 4.

In the remaining 3 options, namely:
1) A is male, B is female
2) A is female, B is male
3) A is male, B is male

Only one suits the male-male bill. ONE. Out of. THREE.

 

[Blind Punk Riot]

I'm sorry, but if any of you go to school still, or college, or university.

Please ask your teacher/tutor this question.

Write the question down word for word and show them it.
They will say 50% and laugh at you, depending on how mean they are.

And they would be wrong.

Or not, since most of mine are geneticists or biochemists quite used to working out the probabilities of inheritance and demanding we do the same.

Then please;
Make my day, take them what you just said. Along with what the question is. Write that down accurately.


I will sit here. Smiling.

 

[Lukeje]

They would laugh at me, but only for bringing them such a simple question.

The sample space has already been said : M/M, M/F, F/M, F/F

Now the events must be sorted correctly; m1: the event that one dog is male.
m2: The event that the other dog is male.

You are told that m1 has occured, therefore the probabilty you want is

P(m2 | m1)= P(m2&m1)/P(m1)=0.25/0.75

And you would be correct.
If you weren't told that one of them is male to begin with.

ONE OF THEM IS MALE.

Therefore you only have the probablity of the other one.


One is male, therefore you discount the odds of that one.
Thats what you do.



Go to them and tell them what you just said aswell
they will seriously lolololololol

But you don't know which one is male, therefore you have to take into account the probability of the other one. The two probabilities are not independant.

 

[Blind Punk Riot]

They would laugh at me, but only for bringing them such a simple question.

The sample space has already been said : M/M, M/F, F/M, F/F

Now the events must be sorted correctly; m1: the event that one dog is male.
m2: The event that the other dog is male.

You are told that m1 has occured, therefore the probabilty you want is

P(m2 | m1)= P(m2&m1)/P(m1)=0.25/0.75

And you would be correct.
If you weren't told that one of them is male to begin with.

ONE OF THEM IS MALE.

Therefore you only have the probablity of the other one.


One is male, therefore you discount the odds of that one.
Thats what you do.



Go to them and tell them what you just said aswell
they will seriously lolololololol

But you don't know which one is male, therefore you have to take into account the probability of the other one. The two probabilities are not independant.

You're telling me, that because the first dog, you can hold that one in your hand. Thats male.

Ok. You know that is male.

How many dogs are left there.
theres one there.

It can either be male, or female.
the dog youre holding can only be male.


why would you put the male dog down, and pick up the female dog. proclaiming that that makes a different odd?

clicked?


Now I can die in peace.

Someone help me out here...

 

[irrelevantnugget]

Seriously, Riot.
How can you just say that everybody should be entitled to his/her own opinions, then blatantly say that everybody NOT saying 50% is wrong?

Also, WE HAVE EXPLAINED IT.
READ IT. TRY TO UNDERSTAND IT.

This will be my last post in here, because some people simply can't think for themselves and go with the mob, and this is simply infuriating me.

Just ADMIT that you're wrong for a change, there's NOTHING wrong with that.

Am I being a hypocrite now? No. This is math, not ethics. Math is an exact science: this means that there is one answer, and ONLY one, if you're asking a simple question, at least. 1+1 is not either 2 or 3, it clearly is 2.

I understand the matter of this question, I understand the answer, and professors have calculated this and say this is a fact.

SO.

2 dogs. 4 possibilities:
1) A is male, B is female
2) A is female, B is male
3) A is male, B is male
4) A is female, B is female.

Shopkeeper says that 1 dog is male.
What most people do at this point, is assign the 'male' attribute to Dog A automatically, taking only options 1 and 3 for their 1/2 solution. (That includes you)
It is however, never said that Dog A is that male. The option that Dog A is female, and Dog B was the male the shopkeeper talked about, still exists and should NOT be discarded.

So the only real option that is tossed out the window, is option 4.

In the remaining 3 options, namely:
1) A is male, B is female
2) A is female, B is male
3) A is male, B is male

Only one suits the male-male bill. ONE. Out of. THREE.

Ok, feeling the need to quote myself now, so people would read this. It landed as the last post on page 4, so odds of that being read are pretty low.


Also, don't pm me telling me I'm wrong, Riot. I'm not trying to annoy you, YOU're the one annoying me and winding ME up. Read the post I just quoted. It's in bold. That is where you went wrong in your reasoning.

 

[Lukeje]

You're telling me, that because the first dog, you can hold that one in your hand. Thats male.

Ok. You know that is male.

How many dogs are left there.
theres one there.

It can either be male, or female.
the dog youre holding can only be male.


why would you put the male dog down, and pick up the female dog. proclaiming that that makes a different odd?

clicked?


Now I can die in peace.

Someone help me out here...

OK, the question as it appears to me is 'given there are two dogs, one of which is male, what is the probability of both dogs being male' to which the answer is 1/3.
Edit: upon rereading the OP, the question doesn't make sense; upon knowing that one of the dogs is male, would you not just go 'I'll have that one then' and leave the shop? Why would you care about the other dog's sex?

 

[Blind Punk Riot]

That is where you went wrong in your reasoning.

Ok without wanting to quote your entire thing.

if you have decided Dog A is male, why do you still have a Dog A is female in your remaining odds?



I suggest, you read that carefully, rethink your choice.
I have read what you are saying, and it is unfortunately wrong. I don't get a kick out of correcting people, I just get upset when people don't understand things. And I have really tried to help you out here and explain to you how it is.

But if you don't want to rethink your own statement then thats fine.
Be wrong. Just please go through the humiliation of finding someone you know who is incredibly good at maths and probability for them to tell you you are wrong. Since you can't really trust me, some random person of the internet, that you are wrong.


I feel a throbbing pain in the front of my brain.

 

[TKTom]

That is where you went wrong in your reasoning.

Ok without wanting to quote your entire thing.

if you have decided Dog A is male, why do you still have a Dog A is female in your remaining odds?



I suggest, you read that carefully, rethink your choice.
I have read what you are saying, and it is unfortunately wrong. I don't get a kick out of correcting people, I just get upset when people don't understand things. And I have really tried to help you out here and explain to you how it is.

But if you don't want to rethink your own statement then thats fine.
Be wrong. Just please go through the humiliation of finding someone you know who is incredibly good at maths and probability for them to tell you you are wrong. Since you can't really trust me, some random person of the internet, that you are wrong.


I feel a throbbing pain in the front of my brain.

It's not the event dog A is male. It's the event ONE dog is male that has been found to be true. The event of one dog is male leaves you with 3 outcomes ratehr than just 2.

 

[Ancalagon]

if you have decided Dog A is male, why do you still have a Dog A is female in your remaining odds?

Because he hasn't decided that Dog A is male, he's decided that a Dog is male. That's the subtle distinction that is at the heart of this problem.

 

[Lukeje]

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
This link gives the solution; assuming that you don't know which dog is male, the question is the same as Q2, but if you label the dogs, then it is equivalent to Q1.

 

[irrelevantnugget]

That is where you went wrong in your reasoning.

Ok without wanting to quote your entire thing.

if you have decided Dog A is male, why do you still have a Dog A is female in your remaining odds?



I suggest, you read that carefully, rethink your choice.
I have read what you are saying, and it is unfortunately wrong. I don't get a kick out of correcting people, I just get upset when people don't understand things. And I have really tried to help you out here and explain to you how it is.

But if you don't want to rethink your own statement then thats fine.
Be wrong. Just please go through the humiliation of finding someone you know who is incredibly good at maths and probability for them to tell you you are wrong. Since you can't really trust me, some random person of the internet, that you are wrong.


I feel a throbbing pain in the front of my brain.

That's just it. I HAVE NOT DECIDED THAT DOG A IS MALE.
There is still a 1/3 chance that Dog A is female, thus Dog B being male.

I'm getting upset over your idiocy here.

Also, I'll just leave this here:

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.

 

[Blind Punk Riot]

...really now... please draw and cut out four dog shapes.

write male on two of them, write female on the other two.

Hold in your hand one called male.
Thats the one you have been told is male.

look at the three you have remaining, you should have two females and one male.
So the dog is either female, REALLY REALLY FEMALE, much like it is female already, and male.

thats ignoring the fact you should have removed the one saying female on it anyway. since you have a choice of male or female.



Is that a better way to explain it?

Do it at home yourself. but becareful with the scissors, and probably use a soft pencil like a 2b or something, you don't want to hurt yourself.

Probably best to have an adult help you too. Health and Safety is key!

 

[Lukeje]

...really now... please draw and cut out four dog shapes.

write male on two of them, write female on the other two.

Hold in your hand one called male.
Thats the one you have been told is male.

look at the three you have remaining, you should have two females and one male.
So the dog is either female, REALLY REALLY FEMALE, much like it is female already, and male.

thats ignoring the fact you should have removed the one saying female on it anyway. since you have a choice of male or female.



Is that a better way to explain it?

Do it at home yourself. but becareful with the scissors, and probably use a soft pencil like a 2b or something, you don't want to hurt yourself.

Probably best to have an adult help you too. Health and Safety is key!

Correction: Take 8 cardboard cutouts. Call 4 male, 4 female. Remove two females. Now work out probability of two males.