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A Problem Even The Wizard Can't Solve (I hope!)
| October 27th, 2011 at 3:56:46 PM permalink | |
| boymimbo Member since: Nov 12, 2009 Threads: 12 Posts: 2533 | Geez, eh, and he posed as a Canadian, eh? Perhaps I am statman. -----
You want the truth! You can't handle the truth! |
| October 30th, 2011 at 7:48:22 AM permalink | |
| weaselman Member since: Jul 11, 2010 Threads: 17 Posts: 1924 |
Back on topic. Why are we multiplying these probabilities? Clearly, they are not independent. For example, if A,B, and C all are telling the truth, then the probability of D telling the truth is 1, not 1/3. "When two people always agree one of them is unnecessary" |
| October 30th, 2011 at 8:32:28 AM permalink | |
| Mosca Member since: Dec 14, 2009 Threads: 74 Posts: 1628 |
I still contend that as soon as statman misquoted the problem, this became the answer. All the other statements became dependent on the fact that D tells the truth 1/3 of the time, rather than the other way around. NO KILL I |
| October 30th, 2011 at 11:37:47 AM permalink | |
| MathExtremist Member since: Aug 31, 2010 Threads: 46 Posts: 2521 |
I don't think statman misquoted the problem. The two givens are (1) A, B, C, D tell the truth with p(1/3) independently, and (2) A affirms that B denies that C declares that D is a liar. The question is "what is the probability that D is telling the truth if both (1) and (2) are true". Here's a writeup I found in Google Books: "Eddington", by S. Chandrasekhar Eddington calculated the result of 25/71 (correctly, under his assumptions, despite what statman said before). I arrived at 13/41 under a different set of assumptions, namely that A through D all said something relevant. "In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563 |
| October 30th, 2011 at 2:36:45 PM permalink | |
| Garnabby Member since: Aug 14, 2010 Threads: 4 Posts: 197 |
God, having said nothing to date, has never spoke the truth? Interesting. Maybe silence is the only real truth/lie. Why bet at all, if you can be sure?
Anyway, what constitutes a "good bet"? - The best slots-game in town; a sucker's edge; or some gray-area blackjack-stunts?
(P.S. God doesn't even have to exist to be God.) |
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