Poll: A little math problem
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Rude AND wrong - it's the new killer combination everyone wants!gerrymander61 post=18.73797.829632 said:
The fact that one dog in a random set is male has no bearing on the sex of the other dog, yes. (I don't know why everyone keeps saying "gender" when this is all about looking at nards rather than the dogs' self-identity or which color the adorable bowties around their heads happen to be.)gerrymander61 post=18.73797.829632 said:
However -- and this is something that you have completely missed -- "at least one dog is male" tells you something specific about the set, but is not a definite fact about a specific dog. Discrete math is about using logic systematically, not applying pithy truisms at random even when they don't fit the problem.
-- Alex
They're just making themselves look stupid. If you're going to be wrong, you can at least be quiet about it. Of course, what's the point of them looking stupid if they don't even know they look stupid.werepossum post=18.73797.829823 said:
Congrats, Cheeze. I was actually starting to think you might be carrying on intentionally. It's nice to know that sometimes 19 pages of argument isn't wasted time.
I don't remember the exact wording (over thirty years ago!), but it seemed pretty clear to me at the time. It sticks in my mind still because it seemed very logical to me, but they were really excited that I had figured it out. That test put my IQ at over 200. Then I took some more tests, and it settled at something like 148 or 158. I don't remember the exact final number, but it meant they had discovered not a genius, but rather a flaw in their tests. Turns out that: IQ tests estimate not only how smart you are, but also how old mentally you are; they can't help testing what you know at least as much as how smart you are; and they are wildly inconsistent between tests, especially for children. Of course, what they told me initially was:Cheeze_Pavilion post=18.73797.833305 said:
"We think you may be gifted. Or mildly retarded. Frankly, we won't know until we've done some tests."
When you start from that point, it's hard to get really excited about IQ tests, and when they swing so wildly to and fro... Not to mention, tests like facial recognition, ink blots, and throwing bean bags at little Tic-Tac-Toe tables - Toss Across anyone?
Anyway, that problem is evidently a big deal for an eighth grader. My science teacher then spent a class period on that same problem, with about the same arguments as here. Again, a minority picked 33%. Some of that minority got to take tests too (although not the "are you a retard?" tests, which kind of put my back up) and eventually four of us (in each advanced science class) became our own little sub-class in science. It does go to show the vagaries of life - had I not been constantly in trouble, I wouldn't have been sent to take the tests, which means the little tempest about the logic question wouldn't have come up, which means there would have been no class discussion, which means the advanced class would likely have been selected purely on grades, which means I wouldn't have been in it. Although I don't think it's actually changed my life, come to think of it...
So yes, apparently it is something in the question - maybe not just this particular question, but this general type of question - that is ambiguous or difficult to grasp for the human mind. As I've said, I think it's because the odds of male/female on a single pup are so deeply ingrained in our minds and our minds balk at calculating an answer we already know. I was hoping Fondant and The_Logician would have chimed in on it, too; I'd like to see what they thought about the problem.
You know, what would be really interesting would be to see this same question asked in other languages. For me, in the question "What is the probability that the other one is a male?", the other one clearly means the one which wasn't male when checked, whichever one that was. For you, in the same question the other one clearly indicates that one particular pup has been identified as male and the other one refers to a particular pup by default. It would be fascinating to see the effect of languages on the problem, to see how the degree of specificity inherent within each language affects the perception of those reading the question. I wonder if that study has been done?
If anyone is still reading this thread except Cheeze and I, and is multi-lingual, can you see a difference in your answer based on how the question would be phrased in another language? Or is language too non-specific to really know that without seeing a specific wording?
*SIGH* After twenty pages of bad math, we're reduced to semantics?Cheeze_Pavilion post=18.73797.833276 said:
Yes, the wording of the problem is shitty. Grossly, irredeemably shitty.
However...
In the problem, you asked "Is at least one a male?" This is the only piece of information you have.
The final question does, indeed, mention the "other one." There are at least two ways to interpret it:
1. The problem is poorly worded, but the final question contains a bunch of additional information. This information is not part of the narrative or the dialogue but is carefully concealed in some kind of messy ambiguous antecedent thing.
2. The problem is poorly worded, and the final question could be slightly clearer if it said "both" rather than "the other."
And it's your opinion that #1 is obviously more reasonable...?
-- Alex
The answer is two thirds.
Since this is basically the monty hall problem, you could pretty much find a rigorous proof online using bayes theorem.
We know that of the four possible combinations of genders, we are left with the three of
MM,
MF,and
FM.
Let's choose a dog to be our first dog (go ahead, pick one, the first or the second) , and let the other dog be the "other dog".
Clearly, no matter which dog we pick, 2/3 of the time the other dog is a male, assuming that all of four original events are equally likely.
Since this is basically the monty hall problem, you could pretty much find a rigorous proof online using bayes theorem.
We know that of the four possible combinations of genders, we are left with the three of
MM,
MF,and
FM.
Let's choose a dog to be our first dog (go ahead, pick one, the first or the second) , and let the other dog be the "other dog".
Clearly, no matter which dog we pick, 2/3 of the time the other dog is a male, assuming that all of four original events are equally likely.