Poll: A little math problem

[commander keen]

The answer is two thirds.
Since this is basically the monty hall problem,

Once again, this is not the Monty Hall problem.

Its ok to feel embarrassed that you chose 50%
As long as you now recognize that it is 33%

 

[Alex_P]

I mean, which is it more likely to be, that Puppy Washing Man said "yes" on the basis of having checked the puppies and found a male, or that these puppies came from a Breeder who is lesbian canine phobic?

Well, you have to admit that, for a while, you were pretty much implicitly arguing for the latter. In that side discussion about how to model the problem with an "experiment," I mean.

-- Alex

 

[Alex_P]

My opinion is #3, that the final question does not contain any additional information, but rather, clues us into what the question-asker meant when they were talking about the Puppy Washing Man, that the question asker meant that he checked the pups and was thinking either

A) yeah, the first one I checked was male

or

B) yeah, the second one I checked was male, after the first turned out to be female

rather than responding on a basis of knowledge that they came from Female Pair Screening Puppy Breeder.

Yes, and if the puppy-washer looked at one or both of the puppies to find a male, that gives you 33%.

50% only makes sense if "at least one" actually means "I only have this one puppy to look at and don't know anything about the other one."

-- Alex

 

[guyy]

The answer is two thirds.
Since this is basically the monty hall problem,

Once again, this is not the Monty Hall problem.

No, but it's a similar idea. It's really not that complex, just very counterintuitive. (Many famous eggheads wrote in to argue with the Monty Hall problem's correct solution of 1 in 3, so not understanding this doesn't make you dumb or anything.)

Reading some of the other things you said...one thing to remember is that the "other" dog isn't a specific dog, because which one it is depends on which one the guy examining them is talking about.

Simply put, they can't both be female since one is male, so that possibility is completely eliminated; 3 are left, and only one of these (both dogs male) would mean that the "other" dog is male.

Before asking question: M/M, M/F, F/M, F/F, "other" dog not specified, but each has 50% chance of being male.
After asking question: M/M, M/F, F/M, but which dog the "other" one is depends on which one of these is the actual state of the dogs; and, clearly, the "other" one couldn't be male unless they both are, since we already know the "not-other" one is male. Probability: 33%.

The reason this is similar to the Monty Hall problem, and similarly confusing, is that the answer is only 33% if the gameshow's host always, and honestly, points out a door with a goat (or other undesirable thing) behind it; he doesn't pick a random door and tell you what's there. In the same way, the dog breeder doesn't choose a random dog and happen to discover that it's male; he looks a both dogs and tells you that at least one of them is male.

 

[Alex_P]

Actually, that's what I think you guys were arguing for--eliminating all FF pairs sounds less like Puppy Washing Man inspecting puppies, and more like Breeder Person screening all FF pairs out of the pool.

Remember, I was talking about putting one coin down on the table, heads up, and flipping, well, "the other one." Everyone else was talking about reflipping Tails pairs, as if FF pairs were being screened from leaving the Breeder.

I take offense to being randomly lumped in with anybody who voted for "33%."

"Reflipping" anything is unnecessary, and it's a bad idea as far as producing a simple and functional model is concerned. (It is, however, correct to say that we don't really care about what happens to those FFs -- the calculations basically end up discarding the data for us when we make them.) You should just keep all the results you get.

-- Alex

 

[Alex_P]

My opinion is #3, that the final question does not contain any additional information, but rather, clues us into what the question-asker meant when they were talking about the Puppy Washing Man, that the question asker meant that he checked the pups and was thinking either

A) yeah, the first one I checked was male

or

B) yeah, the second one I checked was male, after the first turned out to be female

rather than responding on a basis of knowledge that they came from Female Pair Screening Puppy Breeder.

Yes, and if the puppy-washer looked at one or both of the puppies to find a male, that gives you 33%.

50% only makes sense if "at least one" actually means "I only have this one puppy to look at and don't know anything about the other one."

Or if it means "I am answering yes on the basis of one of the puppies I looked at that turned out to be male."

EDIT:

Which, let's face it, is common sense.

However many puppies he looked at, whatever they were, he said yes because one of the puppies he looked at was male. The other puppy? Well, that's "the other one" so like I said:

Barack Obama (i.e. that one)/"the other one"
M/M
M/F
F/M
F/F

the one other than "the other one" or Barack Obama or that one or whatever you want to call it is represented by the first column. Removing rows where it is female, we're left with two rows, and therefore, 50%

Sigh. Back to square one...

-- Alex

 

[Graustein]

I think I can see where it'd be 33% and where it'd be 50%, but I'm not sure.
Is it the difference between "One dog is male. Find the probability that both are male" and "One dog is male. Find the probability that the other is also male"?

I've been trying and failing to follow this thread, but I think I have it worked out if what I stated above is the case. If not, then I'm completely lost.

 

[guyy]

As I see it now, to remain true to the question, the matrix has to look like this:

Barack Obama (i.e., "that one")/ The Other One
M/M
M/F
F/M
F/F

clearly the bottom two drop out, and we're left with 50%, right? Anyone got any other way of setting up the matrix when we're being asked about 'the other one'?

Well, if you had read my previous post instead of ignoring it, you would have seen I already responded to this. But here it is again: this isn't the right way to look at it, and it's the same mistake nearly everyone else makes. And the same mistake I made, I should add, when I first looked at this problem. "That one" (or "Barack Obama" in your post) is not always dog 1, and it's not always dog 2. It depends on the case; "Barack Obama" doesn't become a specific dog until the breeder checks for a male dog.

Case M/M: "Barack Obama" could be either one, but it doesn't matter, because the "other" dog must be male since both of them are male.
Case M/F: "Barack Obama" is dog #1, and the "other" one is dog #2, which is female.
Case F/M: "Barack Obama" is dog #2, and the "other" one is dog #1, which is female.
Case F/F: This case is impossible because neither dog is male, which contradicts the breeder's statement.

So, there are only 3 cases that could exist, and the "other" dog is only male in 1 of them. 1 in 3 chance, if all cases are equally probable. Weird, seemingly ridiculous, but true.

 

[werepossum]

"We think you may be gifted. Or mildly retarded. Frankly, we won't know until we've done some tests."

That basically describes the swing in the self-evaluation of my own mental powers at various times during this thread.

Well, if we didn't think we were pretty sharp we wouldn't have spent so much time trying to convince you.

On the other hand, that's from a guy who has actually been tested for retardation, so take it for what it's worth.

 

[werepossum]

SNIP
I've read it, and you're missing the point. The question "What is the probability that the other one is a male?" makes no sense unless we can distinguish between puppies.

Based on the information in the question, in what way can you distinguish between the puppies other than by calling one 'the male' and the other 'the one we don't know about'?

That's at the heart of the problem, I think. Clearly, the question should have read "What is the probability that both pups are male." That I think would have been clear to everyone.

That really does make me wonder about the exact wording of the problem the first time I encountered it.