Originally posted by kbaumenFrom your spurious thread/problem rehash on another forum:
I posted it in a forum where more knowledgeable people are often seen - http://www.physicsforums.com/showthread.php?p=1692641#post1692641
Let's see how it goes there.
X: What if he had shown a gold card?Obviously the objections raised by myself and others are reasonable.
Originally posted by eldragonflyObviously the objections raised by myself and others are reasonable.[/b]The fact that he might have shown the golden side is completely irrelevant to the problem.
From your spurious thread/problem rehash on another forum:[b]X: What if he had shown a gold card?
And you say the problem is rehashed there? In what way? I quoted it from page one in this thread. Show me a difference if you think there is one.
Originally posted by eldragonflyObviously the objections raised by myself and others are reasonable.[/b]lol the whole point is that he DIDN'T. without requalifying any of the information from the original problem, take it at face value. it's a one-time shot problem. he shows you a silver side, and has no actual "certain knowledge" of what the other side is.
From your spurious thread/problem rehash on another forum:[b]X: What if he had shown a gold card?
now ask three questions: (this wasn't in the original problem, but just because the first QUESTION was omitted because of its obvious answer, doesn't mean it can't be asked anyway).
1.) what is the probability that he chose the G/G card? it is 0. because he showed you a silver side, and clearly silver is not the same as gold, therefore it can't be the G/G card.
2) what is the probability that he chose the G/S card?
3) what is the probability that he chose the S/S card?
these answers have been thoroughly done and redone, and at one point even was answered correctly by you, but your assertion that the problem is no good because the problem doesn't say what the player WOULD have done if he chose gold instead of silver? a useless and irrelevent (see what i did there) idea. this is a one-time, real world, application of the idea of conditional probability, and the question of what would he ask if he chose a gold card has no bearing on this problem.
imagine what would happen if he said "if the guy picks the gold/gold, he'll take a dump in your hat." it doesn't matter. he DIDN'T PICK gold/gold. the gold/gold card (except insofar as its removal) has no bearing on the answer as the question is posed, and so you have a clean hat. wear it proudly.
Originally posted by eldragonflydefinitely not. you see, the bayesian solution is one way of recognizing that since we have new information (the fact that the probability of the G/G card being the one chosen goes from 1/3 down to 0, because we see a silver side) that the relative probabilities of the other two cards undergo a shift in their likelihood. since the S/S card has twice as many silvers as the G/S side, it is twice as likely to be the card whose silver side you are looking at. and since G/G now has a probability of zero (not because of the problem setup, but because in this real time event you have obtained new information that invalidates the possibility of G/G being the one you're looking at) the other two have to take up the slack.
then obviously you agree that the bayesian solution as given is in error.. 🙁
so now you have two pieces of information: firstly, that the probability of the double silver + the probability of the silver/gold must equal 1. this is because there is no other possible card you could be looking at.
secondly, the S/S card is twice as likely to be bearer of the silver you are looking at. if you want to use algebra to solve you can, but intuition is as valid a method of solution. you are looking for two numbers that add up to 1, and one of which is twice as large as the other. clearly this is 2/3 and 1/3... the relative probabilities that have been arrived at time and time again.
bayes applies perfectly here, and it has nothing to do with whether or not the problem WOULD HAVE changed if the card guy picked a gold side. that's entirely irrelevant. not "discluded." irrelevant.
Once again, I return after work to find another 6-7 pages of the same old stuff.
To eldragonfly: The reason you see us arguing the same "tired old" points and arguments is because they are the ones which are applicable and relevant to the problems at hand.
But I think perhaps I see something of your reasoning, so let me go directly to that..
Combinations - Unless combinations are being specifically and directly chosen, as opposed to components of combinations being assembled randomly, there is no reason to presume all combinations are equally likely.
If I toss 4 fair coins, I don't assume that 4 heads has the same chance as 2 heads and 2 tails. If I did that would be fallacy.
If I toss two fair coins, 1 heads and 1 tails occurs 50% of the time, but the other two combinations only occur 25% of the time each. Three combinations, but not equally likely.
Assuming equality - Just because there are two possibilities does not mean those two possibilities are equal. They must either be proven equal, or else the problem has to state they are equal as a given.
Identical distinctions? - Just because two things are identical in appearance does not mean they can't be considered as distinct from each other when analyzing the problem.
If I had a bag with 10 identical marbles, only one of them is black while the other 9 are white, then I would consider each white marble distinct when looking at the problem, even though I can't actually visually distinguish one of them from any other.
And yet in an identical sort of logic, you have considered both the silver sides of the all-silver card to be the same side in terms of analyzing that problem.
You have also considered girl-older-than-boy to be the same case as boy-older-than-girl.
In looking at any probability problem, you should try to be thorough in examining all possible information pertaining to the result.
For the card problem, this means visible side AND hidden side, and not just "this card". Alternatively, you could consider it by card chosen and side chosen, then note the hidden side for your results calculations.
For the family problem, this means considering which one was born first, rather than merely the combination.
At the very worst, you'll find that the extra details didn't matter and you simply took a longer route to arrive at the same answer.
Separating Set-up from Results - The factors which define how the problem is set-up all occur before the event, and define the full 100% sample space with all possible results. When you examine setup, you want to ignore any information on the results until you have a firm grasp of the odds in the setup. Any information on the results (silver side facing up, at least one boy) can be considered after this.
If you've made a thorough examination of the setup and have marked odds for every result, then you can go through with the information on the results and remove those possibilities which don't fit.
It didn't happen, so it doesn't matter. - In a problem which states results are fair and random, the fact that it COULD have happened can make a difference. However, if you approach it by setup THEN results information, you'll have tossed the possibility anyways.
Nobody here has argued that it could be the gold card given the side showing, neither is anyone arguing the family could have two girls given there was at least one boy.
Originally posted by geepamoogleYour see-through simplistic explanations and continuous personal attacks are hardly relevant. Or insightful. No, just more bogus re-interpretations and faulty reconstructions... of a simple word problem. And it is the others here who cannot properly tell this is nothing more than a simple problem in combinatorial maths. And as for the family problem that was not explicity stated, a reasonable person could easily come to the same conclusion, the language used was rather sloppy and ambiguous.
Once again, I return after work to find another 6-7 pages of the same old stuff.
To eldragonfly: The reason you see us arguing the same "tired old" points and arguments is because they are the ones which are applicable and relevant to the problems at hand.
But I think perhaps I see something of your reasoning, so let me go directly to that..
[b ...[text shortened]... is anyone arguing the family could have two girl given there was at least one boy.
Originally posted by eldragonflyExplanations do not have to be complex to be correct. Simple explanations can also be correct, and complicated solutions can be wrong.
Your see-through simplistic explanations and continuous personal attacks are hardly relevant. Or insightful. No, just more bogus re-interpretations and faulty reconstructions... of a simple word problem. And it is the others here who cannot properly tell this is nothing more than a simple problem in combinatorial maths. And as for the family problem tha ...[text shortened]... son could easily come to the same conclusion, the language used was rather sloppy and ambiguous.
Also, can you tell me where in the above post I have made any sort of personal attack. My comments above have been limited to my understanding of your reaasoning in the two main problems of contention, and where I think you are erring.
I don't know you personally and cannot speak with any authority about your person, although your conduct here speaks very poorly about it.
You see my arguments listed above. Tell me what your counters to the arguments are.
And since you think the family problem is ambiguously worded, I would be interested in hearing your rewording of the problem to resolve the ambiguity you see.
I want more than rhetoric here, I want something solid to respond to.
Originally posted by geepamoogleBut you seem determined to ignore my reasoning and commonsense objections, dismissing them out of hand, it is exactly this kind of hypocritical mish-mosh that i find absurd. This is nonsense, the juvenile baiting was unnecessary, it was often included in almost every rather ambiguous and horribly redundant "foolproof" explanation. You seem eager to include yourself in this group, fact is your nonsensical insights and circular criticisms prove nothing. Put away your crystal ball.
Explanations do not have to be complex to be correct. Simple explanations can also be correct, and complicated solutions can be wrong.
Also, can you tell me where in the above post I have made any sort of personal attack. My comments above have been limited to my understanding of your reaasoning in the two main problems of contention, and where I th the ambiguity you see.
I want more than rhetoric here, I want something solid to respond to.
Originally posted by eldragonflyhe's not ignoring your reasoning and commonsense objections... he's merely noting that you haven't PRESENTED ANY. you say things like "fail." and "wrong." and "circular criticism" and rely on refutations like "the wording is ambiguous" and many other ways of saying that.
But you seem determined to ignore my reasoning and commonsense objections, it is exactly this kind of hypocritical "reasoning" that i find absurd. This is nonsense, the juvenile baiting was unnecessary, it was often included in almost every rather ambiguous and horribly redundant "foolproof" explanation. You seem eager to include yourself in this group, ...[text shortened]... your nonsensical insights and circular criticisms prove nothing. Put away your crystal ball.
but what you fail to do in every instance is actually explain WHY you think the wording is ambiguous, and exactly HOW that leads you either to a response differing from the original question, or to a conclusion that the intended result to the question is ill-gained or false.
these are our objections. not your being correct or incorrect - we honestly couldn't care less except to maybe help analyze where you went wrong if you are incorrect, or to change our own understanding or knowledge if WE indeed are incorrect. but we can't do either of these things when you resort to calling our genuine interest in resolving our differing opinions regarding the validity of the question (not to mention the validity of the result) "nonsense.. juvenile baiting." that's what sets off this tailspin.
and i'm starting to think, based on your repeated denials and your repeated refusal to engage in a clear and unambiguous, substantiated argument, that you have ulterior motives in your response to these forums. maybe you're messing with us, maybe you get off on it, maybe you're being sincere.
it's hard to tell, but i truly hope you make the concession we are asking of you - to present where the question is ambiguous, or what exactly your "commonsense objections" are, so as to get past this infighting and actually get back to some real analysis of interesting probabalistic and mathematical reasoning and conclusions.
Originally posted by eldragonflyAgain, give me some arguments of substance rather than simply rhetoric. I have done my best to draw from your comments the substance of your thinking process, and to address it directly as possible.
But you seem determined to ignore my reasoning and commonsense objections, dismissing them out of hand, it is exactly this kind of hypocritical mish-mosh that i find absurd. This is nonsense, the juvenile baiting was unnecessary, it was often included in almost every rather ambiguous and horribly redundant "foolproof" explanation. You seem eager to inclu ...[text shortened]... s your nonsensical insights and circular criticisms prove nothing. Put away your crystal ball.
I have given you substantive reasoning processes and a representation of what I find to be sound logic in dealing with problems like this. I have given a target to wield your ammunition against, so counter the points I made above.
You have stated that my problem was ambiguous. Give me a corrected wording which removes this ambiguity.
Originally posted by geepamooglei already have, you choose to remain ignorant. i find the rest of your redundant and hollow commentary to be equally worthless and insubstantial.
Again, give me some arguments of substance rather than simply rhetoric.
I have given you substantive reasoning processes and a representation of what I find to be sound logic in dealing with problems like this. I have given a target to wield your ammunition against, so counter the points I made above.
You have stated that my problem was ambiguous. Give me a corrected wording which removes this ambiguity.