BTW, if you ever needed greater proof that Yahoo! Answers is mostly populated by people that only pretend to know what they're talking about: LinkGeeze. All my suspicions are confirmed. Thanks for reminding me why anonymous voting is NOT a good indicator of correctness.
So let's look at it [the Monty Hall problem] again, remembering that the original answer defines certain conditions, the most significant of which is that the host always opens a losing door on purpose. (There's no way he can always open a losing door by chance!) Anything else is a different question. [emphasis mine]in her initial posing of the problem:
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?(Hat tip to Herb Wiskit, who pointed out her error) Well, that is a different question, and it is a different question than the one she answered, and answered incorrectly.
Craig F. Whitaker
Columbia, Maryland
Monty opening the doors does nothing but confuse you. Revealing the no-prize doors in the second set really just distills the second set down to a single high probability choice, instead of n-1 different choices.That's interesting, because it also highlights the fact that the more 'doors' there are, the more compelling the case to switch.
"Then, three objects that are rated equally (say rated 4) are chosen for use in a second stage of the experiment. Note, importantly, that the discreteness of the scale leaves open the possibility that these items might not be perfectly equivalent; for example, a subject may 'truly' rate one of the items 4.1, one 4.26, and one 4.3."Then again, if might be that the subject 'truly' rates both items as exactly 4. Chen isn't just claiming that there might be an undetected preference within the granularity of the initial stage of the experiment, he's going much further and asserting that there necessarily is an undetected preference, in all cases, in that initial stage of the experiment.
"Note that the analysis above assumes that subjects are never completely indifferent between two options; that if pressed they can always decide which of two options they prefer. Economic theory suggests that this is by far the most likely case, but even if subjects can be indifferent (which a discrete rating can never show) the above analysis does not change; the computation simply becomes more difficult."So, what's being overshadowed by his flashy critique of the math involved is that he denies the very basis of the experiment (that any subject can simply not have a preferred ordering of three items). Per the above, he denies this assumption with nothing more than "economic theory suggests that this is by far the most likely case", which, in my book, is at least as piss-poor science as that which he is criticizing.
"Note that the analysis above assumes that subjects are never completely indifferent between two options; that if pressed they can always decide which of two options they prefer."...where "the analysis above" is his initial explanation of the difficulties of the experimental design. His heaviest criticism relies upon the assumption that there is always an initial preference if a subject has "proven" a preference by making a choice (which the experiment does, in fact, force).
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I take one, so now the set is 51.
50 cards are shown to me (?) that are not the ace I am looking for
I am left with 2 unknown cards, the one I have and the one not know to me. Isn't it obvious I have 1/2 prob of picking the right one, because the unknow set has been reduced from 51 to 2 ? Or am I missing something ?
*keeps on reading*
posted by elpapacito at 6:22 PM on April 8, 2008