Poll: A little math problem

[Samirat]

A.
Investigated and Referred to Cup/Uninvestigated, Other Cup
Even/Even
Even/Odd

B.

Investigated and Referred to Cup/Investigated and Other Cup
Even/Even
Even/Odd

Have you gone through a level of math in school where you know what a permutation is? Well, this has to be treated permutatively. Order does matter. And for an even and an odd, because there are two different arrangements for this, both Even Odd and Odd Even must be considered,

No, the order that matters is the one that keeps the possibilities lined up with the correct labels. That's why you can't put "Odd/Even" in there because then you've got an "Odd" under "Investigated and Referred to Cup" and that conflicts with the information given in the word problem.

Tell me, how are your even even answers different? When you investigate the first cup, if it an even, you refer to A. So if you investigate the second cup, it must mean that the first cup was odd.

 

[Ancalagon]

Puppy 1/Puppy 2
M/M
M/F
F/M
F/F

the same as this

Puppy 2/Puppy 1
M/M
M/F
F/M
F/F

Yes, it's totally the same. But it's not the same as:

Referred to Puppy/Not referred to Puppy
M/M
M/F
F/M
F/F

While the objects have not been interacted with, you can swap them if you like. But once observations have been made, you can't swap them, unless you can prove that the observations were entirely inconsequential.

What about my post no. 363? Do you disagree that the situation is as I describe in the first of my statements, i.e. "you could mean that "I've won either bet 1 or bet 2" and maintain that the real situation is one of the other two?

 

[Samirat]

Once you have an order, though, you have to stick with it. You can't change it halfway through, like you're doing. Essentially what you're going in the second one is just relabeling them. But once the problem's started, they can't be reassigned on a whim. For instance, MF is not the same thing as FM. Even when assured that one is heads, they aren't the same.

Uhh, I'm not the one doing changing halfway through--you are: "So, what if he uses the second puppy as the warrant for his response." [http://www.escapistmagazine.com/forums/jump/18.73797.815993]

How is that changing orders? Which one is the warrant for his response is irrelevant, it's still the second dog and the first dog. What you are doing is assigning them an order based on knowledge which you do not, in fact, have, namely, which puppy is the male that the washer was basing his claims on.

By the way, could you check out my question about the information difference in Post 357. It might give you a little uneasiness, which would be helpful.

 

[Jumplion]

What the hell, this topic's still going?!?!?

Havn't we found a solution yet people?

 

[Samirat]

It would appear that the only way to recreate the problem is to flip both coins at the same time. If they're both tails, it's irrelevant to the problem.

Dude, you CAN'T make up a model and then say 'oh, never mind the nonsensical results we get-just ignore them'. If you're getting nonsensical results and you have no explanation for them, then you can't trust your model yet.

They're not nonsensical, they're something which did not, in fact happen. Just like in the question at the beginning, there is a chance that the washer woman will say that both are female. In this case, both could be tails. The fact that one was a male in that particular case doesn't matter. It's like if you asked, out of a group of 100 dogs, if 50 were male. They could say yes, but they could just as easily say no. If I propose a problem where the answer happens to be "yes," it doesn't mean that the answer is always "yes." So if I recreate the experiment, and the answer is "no," it's merely a separate case, and irrelevant to the problem.

EDIT: If you recreated the original problem, with two random dogs of unknown gender, as the problem specifies, would the answer always be "yes?"

 

[Samirat]

I just noticed something, anytime in an argument when someone pulls "The majority believes its right" as evidence to the validity of something; I'm going to send them here to look at that poll.

Hehe, true dat.

 

[Alex_P]

Compare these two scenarios:
A. Your friend looks under one of the cups and says you have won at least one of your bets.
B. Your friend looks under both cups and says you have won at least one of your bets.

Do you see why A actually provides you with more information than B?

Yes, but I fail to see the relevance to the problem--check the OP: the word problem doesn't give us any information by which to figure out whether the Puppy Washing Man checked one puppy and then said yes, or both puppies and then said yes.

I agree totally--it's just that your example gives us more information about the situation than we have in the question under discussion, and therefore, isn't a good fit.

What are the probability matrices of these two scenarios?

A.
Investigated and Referred to Cup/Uninvestigated, Other Cup
Even/Even
Even/Odd



B.

Investigated and Referred to Cup/Investigated and Other Cup
Even/Even
Even/Odd

This business with referents is messing it up.

Here's a simpler one to consider:

You have a number-generating machine. It generates numbers based on the following known probability distribution:
25% 2
50% 1
25% 0

You press the button on the machine. Then your friend looks at the output and says "well, it's a positive number." What's the probability that machine output is 2?

-- Alex

 

[Samirat]

I don't understand. The problem I get. What I don't understand is how this has eleven pages when the answer and a good explanation were stated multiple times on the first page.

Actually, I don't think that many people even got it on the first page. Mostly it was just a torrent of 50 percents. That's the intuitive answer. If there's one thing to understand about problems like these, it's that they're non intuitive. So if the question seems ridiculously simple, take a closer look.

 

[Samirat]

Here's a simpler one to consider:

You have a number-generating machine. It generates numbers based on the following known probability distribution:
25% 2
50% 1
25% 0

You press the button on the machine. Then your friend looks at the output and says "well, it's a positive number." What's the probability that machine output is 2?

-- Alex

So it creates two 0/1's? That's genius. I love it. Saying it is a positive number guarantees at least 1 "1," so it fits perfectly.

Yeah. Sweet. Chomp on that one.

 

[Samirat]

You never responded to my information question on post 357. I would still like your thoughts.

 

[Ancalagon]

What about my post no. 363? Do you disagree that the situation is as I describe in the first of my statements, i.e. "you could mean that "I've won either bet 1 or bet 2" and maintain that the real situation is one of the other two?

Glancing back on it quickly, I guess--what's your point?[/quote]

That if you follow the logic that follows from situation A, i.e. that "I've won either bet 1 or bet 2"

bet1/bet2
M/M
M/F
F/M

then the chance that there are two males is 33%, whereas if you follow your original logic, that you've either won bet 1(situation B), or you've won bet 2(situation C)(both of which you've since stated you can't prove):

Then either

bet1/bet2
M/M
M/F

or:

bet1/bet2
M/M
F/M

 

[Samirat]

It would appear that the only way to recreate the problem is to flip both coins at the same time. If they're both tails, it's irrelevant to the problem.

Dude, you CAN'T make up a model and then say 'oh, never mind the nonsensical results we get-just ignore them'. If you're getting nonsensical results and you have no explanation for them, then you can't trust your model yet.

They're not nonsensical, they're something which did not, in fact happen. [/quote]

If your model is supposed to recreate what happened, and you get results that did not happen, then yes--the results are nonsensical and they need to be explained.[/quote]

The question assumes a random pair of dogs. This alone ensures that sometimes, the washer woman will say "no." In this particular instance, the washer woman said "yes." Therefore, you base your probabilities off of other particular instances, where the washer woman says "yes." They aren't "results" when the situation is different. They just aren't the same problem. They aren't nonsensical, they're just a different case from the premise stated in the problem. You can't have "results," since the problem doesn't even apply to situations where the washer woman says "no."

Again, back to the 100 dogs, magnified example. If I have 100 dogs, and ask if 50 of them are males, and the answer is "yes," it doesn't mean the answer will always be "yes," for a random set of 100 dogs. I could still propose a problem based on the premise that in one instance, the answer was "yes."

 

[Samirat]

You never responded to my information question on post 357. I would still like your thoughts.

You're hung up on the first element on a matrix representing the first element in time. That's where you're misunderstanding me.

You're not answering my question. I'm asking how you can justify the probability being the same, when in one case you're receiving more information than in the other.

[
It is; unfortunately any problem without that step of knowing one result doesn't capture what's being expressed in the original problem, so a machine that only spits out one number isn't an equivalent for the issue raised by the original problem.

No, it's equivalent. Say that it instead spits out two pairs of binary toggles: 0 and 1. So saying it is positive is the same thing as guaranteeing at least one "1."