Poll: A little math problem

[geizr]

It can't be both 50 percent and 33 percent because of semantics. Only a difference in understanding of the premise could accomplish that

Semantics have nothing to do with the understanding of a premise? In a word problem?

Next you'll tell me decimal points have nothing to do with the understanding of a base value in mathematical equation! ;-D

Right, right. But this particular misunderstanding over semantics, about "the other dog," doesn't affect how you set up the problem. And if you can set up the problem correctly, you can solve it. As long as you don't assume the first dog is male, which most of the 50 percenters did, in casual error, you should be fine.

This is what I was trying to get at with Cheeze about the degeneracy of the M/F combination if we use his interpretation of the problem. Even if you force-label dog1 as the male dog, the occurrence of the "other" dog being female has a 2-fold degeneracy. So, that case has to be counted twice if you are going to setup the problem the way Cheeze is proposing. But, even then, you still get 33% for the probability of obtaining both dogs as male. The problem with this method is that it is treacherous because the degeneracy is not immediately obvious. Whereas, just explicitly writing down the different configurations with dog1 and dog2 allows you to find the correct answer without having to make strange assertions(like force-labeling) or clobbering your brain with hidden degeneracies.

 

[Ancalagon]

So say Dog 1 is an English Beagle, and Dog 2 is an American Beagle, then the American Beagle couldn't be male while the English one is female, since that configuration (FM) doesn't look like any option available in the new set of configurations?

I don't know, because that is a different problem. We can make up any kind of adjectives we like to describe the pups and differentiate them, but, unless there's a basis for doing so in this word problem, you're answering a different question.

The reason that I put the adjectives in there is to demonstrate that you have to know which specific puppy is male to get the answer 50%. You say that by putting in the adjectives I'm changing the nature of the question, so:

Question 1:

"There are two puppies. We are informed that at least one of them is male. What is the probability that they are both male?"

Question 2:

"There are two puppies, an American Beagle and an English Beagle. We are informed that at least one of them is male. What is the probability that they are both male?"

Do these two questions have a different set of probabilities of outcomes?

 

[Ancalagon]

Question 1:

"There are two puppies. We are informed that at least one of them is male. What is the probability that they are both male?"

Question 2:

"There are two puppies, an American Beagle and an English Beagle. We are informed that at least one of them is male. What is the probability that they are both male?"

Do these two questions have a different set of probabilities of outcomes?

Maybe, but, I don't see the relevance of those questions to this one:

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?

which is the one we were asked :-D

The reason I asked those two questions, rather than the original one, is that I'm trying to understand where we're diverging. Question 1 is how I see the original question with all of the ambiguity and filler taken out. If you think that the answer to Question 1 is 50%, it's a maths thing. If you think it's 33% then we're understanding what's going on in the original question differently. If it is about the maths, Question 2 is to see if the difference is resolved if it is made more obvious that the dogs cannot be interchanged for the convenience of any calculations. What would you say the answers to Question 1 and Question 2 are?

 

[FrcknFrckn]

Yikes, I check back to see if anyone has come to their senses, and find 3 more pages... now we're arguing about semantics? Never mind that the question doesn't actually impart any new information to the situation, it really doesn't change the outcome at all:

-

Ok, allow me to play the part of the washer.

I have 2 dogs here at my washing shop, A and B. You ask me whether one is male. I answer yes. You then try to determine the probability that the OTHER ONE is male.

There are 4 possible dog combinations here:

1. A is female, B is female. (00)
We can automatically ignore this - as I have already told you that one dog is male, this could not possibly be the case.

2. A is male, B is female. (10)
So yeah, this is a valid case. So the dog I was talking about is dog A, and the 'other dog' must be dog B. Since B is not male, the 'other dog' in this case is not male.

3. A is female, B is male. (01)
Again, this is a valid case, just like #2. So the dog I was talking about is dog B, and the 'other dog' must be dog A. Since A is not male, the 'other dog' in this case is not male.

4. A is male, B is male. (11)
Again a valid case. But which dog was I talking about, A or B? IT DOESN'T MATTER. Heck, I might even be done with the washing, and not remember which was which. If I was talking about A, then the 'other dog' was B. If I was talking about B, then the 'other dog' was A. Either way, the 'other dog' was male.


So, we have 3 equally likely situations left after we rule out #1 - 2, 3, and 4. And of those three, only one has 2 male dogs.

1/3 = 33%.

 

[FrcknFrckn]

Yikes, I check back to see if anyone has come to their senses, and find 3 more pages... now we're arguing about semantics?

You're right--arguing about semantics when discussing a word problem makes as much sense as arguing about whether there's a green zero on a roulette wheel when discussing casino odds.

Oh wait...

I mean, is it really that difficult to see that when you answer a word problem, you need to answer the actual problem posed by the words?

Is it really difficult to see that you're reading more into the words 'other one' than are there? If you'd read the rest of my post, you'd see that those words make absolutely no difference whatsoever.

 

[Anarchemitis]

Man, this is the most full poll I have ever seen on this website.

 

[Alex_P]

And, semantically, I think the parsimonious reading is the one that assumes that "the other" refers to the sex of the second dog independent of which dog it happens to be (analogous to saying "Is there a second male?") rather than the ones that modifies "at least one" to mean "this specific one."

-- Alex

 

[FrcknFrckn]

The other what? The question was about a pair--saying 'the other one' makes no sense. That's like if someone asks you if you'd like french fries or baked potato, and you go 'the other one, please'.

No, it's more like if I have a penny and a quarter, one in each of my hands. I tell you one of my hands has a penny in it, and you ask for the coin in the OTHER HAND. Which hand is it, left or right? That's correct, you don't know - because talking about the OTHER HAND doesn't actually tell you which is which. I can't emphasize this enough: it doesn't give you any knowledge whatsoever about which hand I was referring to.

 

[Alex_P]

And the parsimonious reading is also that when Puppy Washing Man goes "Yes!" he means that either both dogs are male or a specific dog in a male/female pair is male, not that he has knowledge that they are from Guaranteed Lesbo Free Puppy Pairs Breeder or some other kind of knowledge that there was screening of the FF pairs.

Of course.

... And that's how you get 33%.

-- Alex

 

[iain62a]

"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"

Could this include the guy that was cleaning them too? maybe it's a trick and none of the dogs are male