Poll: A little math problem

[Lukeje]

Now, if you want to say this is a brain teaser and "the other one" is meant to be ambiguous, then the whole problem breaks down. Why? Because there are two possible reasons why the Puppy Washing Man could have said "Yes!" which I detailed above. One is where the sign and the reference are both the set, in which case the answer is 33%. The other is where the sign is the set and the reference is at least one specific male puppy, which means the sign is the set and the reference is the specific male puppy, in which case the answer is 50%

And this is where I have been disagreeing with you Cheeze that you don't get 50%. The reason is that there is a degeneracy in the male/female reference because the signs can be interchanged. Having one sign male and one sign female has two unique configurations, whereas the male/male signs have only one unique configuration. So, the male/female reference contains a 2-fold degeneracy that you have to account for, while the male/male reference does not. This is why you still get 33%, even if we take your interpretation.

Unless you also remember that there is a two-fold degeneracy in the male/male;
male1 male2
male2 male1
are degenerate if you label the puppies.

 

[geizr]

Now, if you want to say this is a brain teaser and "the other one" is meant to be ambiguous, then the whole problem breaks down. Why? Because there are two possible reasons why the Puppy Washing Man could have said "Yes!" which I detailed above. One is where the sign and the reference are both the set, in which case the answer is 33%. The other is where the sign is the set and the reference is at least one specific male puppy, which means the sign is the set and the reference is the specific male puppy, in which case the answer is 50%

And this is where I have been disagreeing with you Cheeze that you don't get 50%. The reason is that there is a degeneracy in the male/female reference because the signs can be interchanged. Having one sign male and one sign female has two unique configurations, whereas the male/male signs have only one unique configuration. So, the male/female reference contains a 2-fold degeneracy that you have to account for, while the male/male reference does not. This is why you still get 33%, even if we take your interpretation.

Unless you also remember that there is a two-fold degeneracy in the male/male;
male1 male2
male2 male1
are degenerate if you label the puppies.

You are correct if we have the state labels male1 and male2. However, that is imposing additional information because we don't actually have such state labels. We don't have a first male and a second male designation. Instead, we only have the state labels male and female, no indication of ordering. So, we would have dog1 in the state of male with dog2 in the state of male, or dog2 in the state of male with dog1 in the state of male. No degeneracy because in exchanging dog1 and dog2, I obtain the same configuration. So, there is only one unique configuration where there are two males. Compare this to dog1 in the state of male with dog2 in the state of female, or dog2 in the state of male and dog1 in the state of female. Exchanging the dog1 and dog2 labels does not reproduce the same configuration that you originally start with. Therefore, there are two unique configurations in which there is one male and one female, hence the reason for the degeneracy. So, there is one unique configuration in which there are two males and two unique configurations in which there is one male and one female; hence, the degeneracy on the male/female combination and not the male/male combination given the information actually available in the problem. This is why I have been contending that even under Cheeze's interpretation, we still obtain 33% as the probability.

 

[xioxenna]

personally i believe that in this day and age; the dog is too young to impose a gender upon it. but i will explain the riddle.

--//**\\explanation of how it is actually 33%//**\\--

i will do what i can to explain this simply.

the chance of "one" dog being male or female is 50% as there are two outcomes,

the chance that two dogs are male, is 25%
please refer to this table to see why...

there are 4 scenarios:
Male+Male (M+M)25%
Male+Female (M+F)25%
Female+Male (F+M)25%
Female+Female (F+F)25%

and to answer the question "the chance that two dogs are male, is 25%"

however, having known that the first was a Male, we can exclude F+F (the first dog wasn't female)

thus leaving us with 3 scenarios, and 33%

(yes i know this isnt a great explanation, as (F+M)would imply the 1st dog was female, but the chance that one is female, is 66% to 33% single sex.

it's called relative probability.

 

[FrcknFrckn]

However, think about this: what if the Puppy Washing Man said yes because he knows they came from a Breeder who goes through pairs of puppies in the 25/50/25 distribution, and picked out a pair as soon as he found a male? Although there are twice as many mixed pairs, half the total males are in all-male pairs, so if you've got a male, chances are just as good that it's in an all-male pair as in a mixed pair, just like in the Three Card Problem.

Gee, and here I thought the fact that the guy is currently washing the puppies would imply that maybe, just maybe, he answered 'yes' because he can see the puppies at that moment? And why would some puppy washer know more about the breeder than, I dunno, the store owner who bought from the breeder in the first place?

This is getting silly. I mean honestly, you've created a fanciful scenario there, but why exactly would anyone assume that's the case when the obvious answer is that it's just a random pair of puppies and the washer checked them when the store owner asked her question?

As long as we're at it, why not just assume that the breeder only sells male puppies and keeps all the female puppies for breeding - but only the washer knows it because the breeder is his second cousin? Then the chance is 100%! I mean, it's obvious once you think about it - the answer must be 100%!

...

...and I've been baited into writing again. Sigh. I'm gonna go steal one of geizr's Guinness Draughts...

 

[Alex_P]

stuff

Go-go misplaced condescension!

-- Alex

 

[geizr]

...and I've been baited into writing again. Sigh. I'm gonna go steal one of geizr's Guinness Draughts...

Yeah, and I let myself get sucked back into this whole debate. And just to answer xioxenna right quick, we've tried that approach with Cheeze. It doesn't work.

** Grabs another Guinness Draught to quiet the nerves. Gladly hands one to FrcknFrckn **

 

[Saskwach]

Okay--I get where he went wrong. I'd still like to know exactly what he meant, though, by set vs. sequential probability.

Without returning to the argument, I'll just say that what he means is this:
Set probability is saying that something is true of the set: there are three apples in this box of seven fruits. There is no ordering here, only information about the whole set.
Sequential probability tells us something about the order: the first three fruits I picked out of the box were apples.

Ahh, okay. And without dragging you back in, it seems he was saying more than that, something like Alex_P is saying in 813.

Oh? I guess that's what happens when I try to 'feel out' technical maths jargon.

 

[FrcknFrckn]

Because it's a word problem, so you can't just go assuming information that is not either in the problem, nor necessarily true because of information in the problem.

Thank you - that is exactly what I was saying in the rest of my post.

So why, exactly, would we start bringing the washer's motivation into things? There is no information about how or why he knows what he knows. As soon as you start talking about his knowledge of the breeder, you are bringing in information that wasn't in the original problem.

This is the sum total of information we have about the scenario:

1. There are two puppies.
2. At least one of the puppies is male.

The text of the problem is simply a story concocted by the problem writer in order to bring that information forward to you.

You seem fixated on making up information about how the washer knows what he knows. Back to my last post: as long as you're creating scenarios where the breeder is giving out puppy pairs that aren't randomly distributed, you can create any scenario you want, such as one where the breeder only sells male puppies. Entirely possible, but completely meaningless, as you're basing your answer on information that wasn't in the problem to begin with.

 

[FrcknFrckn]

And that's it for me. Cheeze is never going to get it, so I'm going to go enjoy my beer in peace, and leave it to more patient people to explain his fallacies...

 

[geizr]

This is why I have been contending that even under Cheeze's interpretation, we still obtain 33% as the probability.

No you haven't: "...he becomes aware of the fact Jesus is male. Because of that specificity of knowledge, the probability of Satan being male is 50%, in that scenario." [http://www.escapistmagazine.com/forums/jump/18.73797.839039] You were every bit as wrong as I was until Alex_P showed us why it doesn't matter even if we know what dog is male.

Yes, I was wrong about what Alex was saying in the scenario he presented, and I admitted that his reasoning was correct for the scenario he presented. However, I actually have been pointing out in several posts that I can use your interpretation and still obtain 33% because of the degeneracy of the M/F combination.

"The sentence you've been pinning your logic on all this time has more than one meaning because of the ambiguities of the English language. Brain teasers take advantage of this ambiguity to cause people who use literal interpretations, such as yourself, to derive precisely the wrong answer." [http://www.escapistmagazine.com/forums/jump/18.73797.840505]

And then you take the information from the problem that reads: 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 and draw from that information that we should:

"Consider this scenario. The Puppy Washing Man picks up one puppy and looks at it and discovers it is male. At that point, he can truthfully answer the shopkeeper in the affirmative that at least one puppy is male. But, it could be that he picks up the first puppy and discovers it is female. So, he must then pick up and examine the second puppy to properly answer the shopkeeper. It is because we don't know what the Puppy Washing Man had to do to determine if there is at least one male that we get 3 total configurations possible." [http://www.escapistmagazine.com/forums/jump/18.73797.838752]

Ever consider the scenario that he doesn't check the puppies, but rather knows that they come from a Breeder that screens out all FF pairs, another way to get 33%? Or that he knows they were selected from a pool with the expected 25/50/25 distribution, and the first male that was picked determined the pair that was selected, and similarly to the logic of the Three Card Problem, that means the probability of an all-male pair is 50%?

You are correct that there are other ways the puppy-washer could know that there are two males. I picked what I thought was the simplest, most obvious way for him to determine that information. Since he is right there with them giving them a bath, he just looks at them. As I understand the problem, we are asking the probability of the male/male combination from the point of view of the person buying the puppy, not from the point of view of the puppy-washer. In my opinion, it is a logic error to impose that the person buying the puppy has knowledge of the selection process leading to the particular pair of puppies when no such knowledge is stated in the problem. You are allowed to assume that such is possibility in the problem, but then I think you would be making the problem more complex than is given by adding information that is not given.

I mean, why does this have to be some big dick waving contest? Why can't it just be smart people trying to figure a problem out in a polite and rational manner?

It was not my intent to turn this into a dick waving contest. I apologize for making you see this as being such. I have been trying to present my logic as best as I am capable to prove the points I have been trying to make. I am not perfect in this, and I admit such. I admit I have said things that have attacked you and caused offense toward you, rather than defense of my own logic. For that, I definitely apologize. Regardless, I still stand behind the logic I have presented and the position I have taken in this entire thread of conversation.

Sure you didn't choke on that Guinness because it was extra cold? What kind of sick person drinks Guinness extra cold? That's like doing jello shots of single malt scotch!

Okay, now that feels like you are trying to attack me personally. I like my Guinness the way I like it. And if you've ever bought the Guinness Draught(the one in the grey bottle), you will see that it explicitly says to serve extra cold. Just because you don't agree with someone doesn't mean that they don't know what they are talking about. And before you try to zing me by saying that's what I have been doing to you, I have not been saying you don't know what you are talking about. I think you are quite knowledgeable of what you are saying. I have only said that your reasoning has an error in it.

We disagree, Cheeze. I think at this point we just need to shake hands and agree that we disagree rather than turn this into a war with further hostilities between us. That would not be good for either of us.

** EDIT: Corrected tagging around one of the quotes