Cheeze_Pavilion post=18.73797.838450 said:
FrcknFrckn post=18.73797.838415 said:
I have two coins, one in each of my hands. I tell you at least one of my hands has a penny in it, and you ask for the coin in the OTHER HAND.
You're changed the question too much. The question states: "What is the probability that the other one is a male?" The reason it tells us something is because it's coming directly from the question-asker, and therefore, gives us a clue as to how to resolve the ambiguity in the rest of the question.
No, it doesn't, Cheeze. This is the constant error in your logic. The "other" does not refer to a specific dog because that requires that we know which is the first dog being referenced as male. And don't say that the problem is poorly worded, because it's not. However, your reading comprehension in this case is definitely in question. Let's break down the problem statement line by line.
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?
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.
We are told there are two beagles, but at this point it is unknown whether they are male or female. So, as far as we are concerned, the beagles can be any one of the combinations male/male, female/female, male/female, or female/male.
You tell her that you want only a male, and she telephones the fellow who's giving them a bath.
We have specified that we are only interested in purchasing a male beagle. However, what is more important is the fact there is someone who has access to both beagles simultaneously to be able to examine them for gender. This person examines the beagles while bathing them and obtains their genders.
"Is at least one a male?" she asks him. "Yes!" she informs you with a smile.
This is the first point where your logic falls off, Cheeze. The shopkeeper only asks whether at least one puppy is male, not which one. We don't know at this point if one or both puppies are male. In the case of only one being male, at this point, we don't know which one. We can not force the label on the male one to be dog1. 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.
What is the probability that the other one is a male?
This is where I think I understand how you are misunderstanding the problem statement, and it's not a matter of the question being poorly worded. We are told that at least one puppy is male. By including that the other one be male to obtain the probability, we are asking for the case that both puppies be male. But we don't know which one to start with to assign as being male. So mentally, we must consider two different scenarios: 1) dog1 is the male and dog2 is the other one, 2) dog2 is the male dog and dog1 is the other one. When you work out the outcomes from both these scenarios, you find there are a total of 3 unique configurations, with the male/male configuration being only 1 of the 3.
Your problem, Cheeze, is that you are constantly misunderstanding "the other one" to reference a specific puppy, and it doesn't. What the statement "the other one" is intended to do is to specify that we want both puppies to be male. It can not specify a specific puppy because we don't have a reference to which is the puppy that is known to be male. It is invalid to say that you can just choose one because you can't, precisely because we don't know if the Puppy Washing Man found the first one he picked up to be male or the second one he picked up to be male. Doing so would be to create extra information that is not given in the problem, which would mean that you are the only one who has been changing the problem all this time.
Another thing is that this kind of problem is what is known as a brain teaser. The wording of brain teasers is logically consistent and grammatically correct. But, they take advantage of the ambiguities of the English language to create statements that can be easily misinterpreted if one does not exercise careful reading comprehension. In fact, taking the statements of brain teasers at literal face value, as you have apparently done, will almost always lead you to exactly the wrong answer. You have to read the total context of the problem and comprehend the total action occurring in the problem.
Finally, if you really don't want to believe us, you can look the problem up on wikipedia. The wording is EXACTLY the same (http://en.wikipedia.org/wiki/Marilyn_vos_Savant [http://en.wikipedia.org/wiki/Marilyn_vos_Savant], look for the "Two Boys" problem). You can also check this link http://en.wikipedia.org/wiki/Boy_or_Girl_paradox [http://en.wikipedia.org/wiki/Boy_or_Girl_paradox], where they point out exactly the fallacies in logic that most people who choose 50% make.
