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What's a boy to do?
An interesting problem was recently brought to my attention.
Let us say that you and I are standing next to a table on which I have placed three boards identical in every respect except that each has a different number painted on it.....1, 2, and 3, respectively. I say to you that if you turn your back I will place a five dollar bill under one of the boards and a slip of paper that says "you lose" under each of the others. You then turn back to face the table and point to or name the board you think has the five dollar bill under it. If you're right, you win the five bucks. We proceed. You pick, say, board number one. I say, "O.k., tell you what, I like you so I'm going to make this easier for you," and I remove board number three to show you that it has a "you lose" tag under it. Obviously, the five dollars must be under one of the other two. "So," I say, "would you like to stick with your original pick, or change your mind?" It is a given that the game is not rigged in any way and you are not being fooled by anything ambiguous or otherwise misleading in the description. The question.......what should you do? Wolfgang |
What's a boy to do?
Wolfgang wrote: An interesting problem was recently brought to my attention. Let us say that you and I are standing next to a table on which I have placed three boards identical in every respect except that each has a different number painted on it.....1, 2, and 3, respectively. I say to you that if you turn your back I will place a five dollar bill under one of the boards and a slip of paper that says "you lose" under each of the others. You then turn back to face the table and point to or name the board you think has the five dollar bill under it. If you're right, you win the five bucks. We proceed. You pick, say, board number one. I say, "O.k., tell you what, I like you so I'm going to make this easier for you," and I remove board number three to show you that it has a "you lose" tag under it. Obviously, the five dollars must be under one of the other two. "So," I say, "would you like to stick with your original pick, or change your mind?" It is a given that the game is not rigged in any way and you are not being fooled by anything ambiguous or otherwise misleading in the description. The question.......what should you do? Assuming that I trust you, it doesn't matter. It's 50/50 chance you can stick with your current pick or switch. Given it's you, it REALLY doesn't matter since the $5 is probably in your pocket. - Ken |
What's a boy to do?
Wolfgang wrote: An interesting problem was recently brought to my attention. Let us say that you and I are standing next to a table on which I have placed three boards identical in every respect except that each has a different number painted on it.....1, 2, and 3, respectively. I say to you that if you turn your back I will place a five dollar bill under one of the boards and a slip of paper that says "you lose" under each of the others. You then turn back to face the table and point to or name the board you think has the five dollar bill under it. If you're right, you win the five bucks. We proceed. You pick, say, board number one. I say, "O.k., tell you what, I like you so I'm going to make this easier for you," and I remove board number three to show you that it has a "you lose" tag under it. Obviously, the five dollars must be under one of the other two. "So," I say, "would you like to stick with your original pick, or change your mind?" It is a given that the game is not rigged in any way and you are not being fooled by anything ambiguous or otherwise misleading in the description. The question.......what should you do? Assuming that I trust you, it doesn't matter. It's 50/50 chance you can stick with your current pick or switch. Given it's you, it REALLY doesn't matter since the $5 is probably in your pocket. - Ken |
What's a boy to do?
Wolfgang wrote:
An interesting problem was recently brought to my attention. Ah yes, the famous Monty Hall Puzzle. Go ahead & tell 'em the answer; they won't believe it anyway. g Joe F. |
What's a boy to do?
"rb608" wrote in message ups.com... Wolfgang wrote: An interesting problem was recently brought to my attention. Ah yes, the famous Monty Hall Puzzle. Spoilsport. Go ahead & tell 'em the answer; they won't believe it anyway. g Don't have to. You just did. :) Wolfgang |
What's a boy to do?
"Wolfgang" wrote in :
The question.......what should you do? Wolfgang If I recall correctly, you should change your mind. When you chose the first, you had a 1/3 chance of being right, and nothing has changed that. If you change your mind now, that gives you a 2/3 chance of being correct. I'm pretty sure I'm dead wrong on that 2/3 number, though, but the chance is more than 0.5. The key is that the removal process is not random. -- Scott Reverse name to reply |
What's a boy to do?
Wolfgang wrote:
Don't have to. You just did. :) Do not for a moment think that this entire body of flyfishermen & women even approach the level of geekiness necessary to be familiar with the MH puzzle and an extended discussion of the answer. Methinks anyone who already did know of the puzzle recognized as I did; so I doubt I spoiled it for anyone. But for those who would now go look it up by name instead of figuring out the answer would probably fish pegged beads anyway. :-) Joe F. |
What's a boy to do?
"Wolfgang" wrote in message ... An interesting problem was recently brought to my attention. Let us say that you and I are standing next to a table on which I have placed three boards identical in every respect except that each has a different number painted on it.....1, 2, and 3, respectively. I say to you that if you turn your back I will place a five dollar bill under one of the boards and a slip of paper that says "you lose" under each of the others. You then turn back to face the table and point to or name the board you think has the five dollar bill under it. If you're right, you win the five bucks. We proceed. You pick, say, board number one. I say, "O.k., tell you what, I like you so I'm going to make this easier for you," and I remove board number three to show you that it has a "you lose" tag under it. Obviously, the five dollars must be under one of the other two. "So," I say, "would you like to stick with your original pick, or change your mind?" It is a given that the game is not rigged in any way and you are not being fooled by anything ambiguous or otherwise misleading in the description. The question.......what should you do? Wolfgang I'd knock you in the head and take the money. If it wasnt under the boards it would surely be in your pocket along with several other pieces of folding money. Problem solved! "a friend" |
What's a boy to do?
"Wolfgang" wrote in message ... An interesting problem was recently brought to my attention. Let us say that you and I are standing next to a table on which I have placed three boards identical in every respect except that each has a different number painted on it.....1, 2, and 3, respectively. I say to you that if you turn your back I will place a five dollar bill under one of the boards and a slip of paper that says "you lose" under each of the others. You then turn back to face the table and point to or name the board you think has the five dollar bill under it. If you're right, you win the five bucks. We proceed. You pick, say, board number one. I say, "O.k., tell you what, I like you so I'm going to make this easier for you," and I remove board number three to show you that it has a "you lose" tag under it. Obviously, the five dollars must be under one of the other two. "So," I say, "would you like to stick with your original pick, or change your mind?" It is a given that the game is not rigged in any way and you are not being fooled by anything ambiguous or otherwise misleading in the description. The question.......what should you do? Wolfgang The obvious answer is to pick up board no.3, hit you over the head with it, find the $5 ( plus any other spare change you have in your pocket) and leave. 8~ ). Bob Weinberger |
What's a boy to do?
rb608 wrote: Wolfgang wrote: Don't have to. You just did. :) Do not for a moment think that this entire body of flyfishermen & women even approach the level of geekiness necessary to be familiar with the MH puzzle and an extended discussion of the answer. The thought never occurred to me. Trust me. :) Methinks anyone who already did know of the puzzle recognized as I did; so I doubt I spoiled it for anyone. But for those who would now go look it up by name instead of figuring out the answer would probably fish pegged beads anyway. :-) Precisely.......Google. I bumped into this yesterday in a delightful little novel called "The Curious Incident of the Dog In the Night-Time" by Mark Haddon. The narrator, a 15 year old autistic boy named Christopher Boone, relates his adventure as an amateur sleuth (ala his hero, Sherlock) and runaway. He's something of a mathematical savant. As Haddon, through Chrisopher, relates the story, the question was put to Marylin vos Savant in "Parade" magazine by one Craig F. Whitaker of Columbia Maryland. Wikipedia confirms this (while making it clear that this is "a widely known statement" of the problem and thus, presumably, not the first), so I assume that the quotes Haddon provides from responses to Ms. Savant's answer, that you should always change your answer and pick the final door, are also genuine: "I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error."--Robert Sachs, Ph.D., George Mason University "There is enough mathematical illiteracy in this country, and we don't need the world's highest IQ propagating more. Shame!"--Scott Smith, Ph.D., University of Florida "I am in shock that after being corrected by at least three mathemeticians, you still do not see your mistake."--Kent Ford, Dickinson State University "I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for help with future columns."--W. Robert Smith, Ph.D., Georgia State University "You are utterly incorrect...How many irate mathemeticians are needed to get you to change your mind?"--E. Ray Bobo, Ph.D., Georgetown University "If all those Ph.D.'s were wrong, the country would be in very serious trouble."--Everett Harman, Ph.D., U.S. Army Research Institute I started this thread because it was a fascinating problem......not, for me, so much because of the answer (which, naturally, I got wrong) or because of the solutions (which I can sort of dimly comprehend.....for about as long as I am looking at them), but because it is such a truly beautiful illustration of the axiom that it ain't so much what we don't know as what we know that ain't so that ****s us up.....which is, in turn, a simply gorgeous paradox. I posted the quotes included above because, of course, I knew that the usual ****weasels would be incapable of resisting the temptation to make asses of themselves yet again and thus append themselves to the list. More of them would unquestionably have done so if you hadn't netted kennie so quickly. :) Wolfgang "gravy" it's called......and i like it. |
What's a boy to do?
Scott Seidman wrote: "Wolfgang" wrote in : The question.......what should you do? Wolfgang If I recall correctly, you should change your mind. When you chose the first, you had a 1/3 chance of being right, and nothing has changed that. If you change your mind now, that gives you a 2/3 chance of being correct. I'm pretty sure I'm dead wrong on that 2/3 number, though, but the chance is more than 0.5. Actually, I believe your exactly right about the 2/3. :) Um.....well, it's been a couple hours since I last looked at the solution, so I could be wrong. :( The key is that the removal process is not random. Yep. Wolfgang |
What's a boy to do?
Bob Weinberger wrote: The obvious answer is to pick up board no.3, hit you over the head with it, find the $5 ( plus any other spare change you have in your pocket) and leave. 8~ ). Ladies and gentlemen, we have a winner! :) Wolfgang don't forget to torch the place on your way out.......dna is a stone cold bitch! |
What's a boy to do?
basilratbone wrote: I'd knock you in the head and take the money. If it wasnt under the boards it would surely be in your pocket along with several other pieces of folding money. Problem solved! "a friend" Do I know you? Um......aside from your profession, that is. Dumbass. Wolfgang |
What's a boy to do?
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What's a boy to do?
Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? -- TL, Tim --------------------------- http://css.sbcma.com/timj/ |
What's a boy to do?
When you chose the first, you had a 1/3 chance of being right, and nothing has changed that.
Scott, I assume you know what a Tontine is. Suppose you and two friends form one. Overlooking health and age differences and the fact that one smokes and drinks heavily, each of you has one chance in three of winning. Later, one of the others dies. Now, what is your chance of winning? vince |
What's a boy to do?
On Fri, 27 Oct 2006 22:43:52 -0400, "Tim J."
wrote: Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? That could be BAFfling... TC, R |
What's a boy to do?
On Fri, 27 Oct 2006 23:39:09 -0400, "Tim J."
wrote: typed: On Fri, 27 Oct 2006 22:43:52 -0400, "Tim J." wrote: Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? That could be BAFfling... ... but wrong. How? deaf-dead = 2, 2 + bad = baf, no? May not be, but if not, ??? TC, R |
What's a boy to do?
typed: On Fri, 27 Oct 2006 23:39:09 -0400, "Tim J." wrote: typed: On Fri, 27 Oct 2006 22:43:52 -0400, "Tim J." wrote: Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? That could be BAFfling... ... but wrong. How? deaf-dead = 2, 2 + bad = baf, no? May not be, but if not, ??? You never left the room. -- TL, Tim --------------------------- http://css.sbcma.com/timj/ |
What's a boy to do?
On Sat, 28 Oct 2006 00:24:58 -0400, "Tim J."
wrote: typed: On Fri, 27 Oct 2006 23:39:09 -0400, "Tim J." wrote: typed: On Fri, 27 Oct 2006 22:43:52 -0400, "Tim J." wrote: Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? That could be BAFfling... ... but wrong. How? deaf-dead = 2, 2 + bad = baf, no? May not be, but if not, ??? You never left the room. Um, you didn't say "we you in a room and _add_ deaf people..." Phrased the way you originally phrased it, wouldn't I be including in "deaf people?" I'm not a math geek, and I've never heard of this "oldie," I just thought it was more of logic thing with hex - f to d and back to f, but ??? I could understand it if it spelled something, but including me makes it bb0, no? Is that something hilarious to math prof-types or something? TC, R |
What's a boy to do?
"Wolfgang" wrote in message ups.com... Actually, I believe your exactly right about the 2/3. :) Um.....well, it's been a couple hours since I last looked at the solution, so I could be wrong. :( The key is that the removal process is not random. Yep. Wolfgang Yes, the key from a pure mathematical probability standpoint is that the removal process is not random. However, from a human nature standpoint the fact that the removal is not random could also dictate in some circumstances that I should not switch. If the rules are that you must always reveal one of the losers, then the MH problem solution dictates that it is in my interest to switch. However such a rule was not stated in the question you posed. If I suspect that you are aware that I most likely am familiar with the MH problem solution, and if I also think that you think that I am unaware that you have that knowledge then, if you reveal one of the losers, it is probably not in my interest to switch (geez what a tortured sentence). Conversely, with those respective mindsets, if you choose not to reveal one of the losers I probably should switch. Of course after playing a few times in the absence of a rule to always reveal one of the losers, the activity would quickly go to each of us trying to second guess the other. Bob Weinberger |
What's a boy to do?
On Fri, 27 Oct 2006 22:45:54 -0400, vincent p. norris
wrote: When you chose the first, you had a 1/3 chance of being right, and nothing has changed that. Scott, I assume you know what a Tontine is. Suppose you and two friends form one. Overlooking health and age differences and the fact that one smokes and drinks heavily, each of you has one chance in three of winning. Later, one of the others dies. Now, what is your chance of winning? vince Depends somewhat on your and their morality. There's a reason tontines were outlawed... -- Antiquis temporibus, nati tibi similes in rupibus ventosissimis exponebantur ad necem. http://www.visi.com/~cyli |
What's a boy to do?
"Wolfgang" wrote in message ... An interesting problem was recently brought to my attention. The question.......what should you do? Wolfgang When you first picked, you had a one in three chance of being right. With one board removed, your pick 'still' has a one in three (33 1/3 %) chance of being right. However, with only two boards left, you can chance your chances. If you pick a different board (the remaining) you will now have a one in two (50%) chance of being right. it behooves you to re-pick. john |
What's a boy to do?
wrote in message ... On Sat, 28 Oct 2006 00:24:58 -0400, "Tim J." wrote: typed: On Fri, 27 Oct 2006 23:39:09 -0400, "Tim J." wrote: typed: On Fri, 27 Oct 2006 22:43:52 -0400, "Tim J." wrote: Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? That could be BAFfling... ... but wrong. How? deaf-dead = 2, 2 + bad = baf, no? May not be, but if not, ??? You never left the room. Um, you didn't say "we you in a room and _add_ deaf people..." Phrased the way you originally phrased it, wouldn't I be including in "deaf people?" I'm not a math geek, and I've never heard of this "oldie," I just thought it was more of logic thing with hex - f to d and back to f, but ??? I could understand it if it spelled something, but including me makes it bb0, no? Is that something hilarious to math prof-types or something? TC, R I would still knock you in the head and take your money along with the others. I would be the baddest person in the room. there would be a lot of dead people in the room . All those who woud remove them would also be dead. so , the answer is no one alive. I would leave with yours and theirs money. problem solved |
What's a boy to do?
"Wolfgang" wrote in message ... The question.......what should you do? The easiest way to convince yourself of the correct answer (since it's non-intuitive) is to play the game with someone. After a short while, you'll realize that the only way you can get it right if you don't switch is if you picked it right from the beginning - in other words, 1 chance in 3. |
What's a boy to do?
jeffc wrote: "Wolfgang" wrote in message ... The question.......what should you do? The easiest way to convince yourself of the correct answer (since it's non-intuitive) is to play the game with someone. After a short while, you'll realize that the only way you can get it right if you don't switch is if you picked it right from the beginning - in other words, 1 chance in 3. Sure, first they take all yer shiny new nickels....... Hey, I've only got just so many five dollar bills, ya know! :( Anyway, that's right.....so long as we stress the "convince" part, as opposed to learn. Unless and until you become familiar with the correct solution to the Monty Hall problem (whether it's explained to you or you work the logic out for yourself) intuition can lead you down a long and, if it's presented as a betting game, ruinous road. Wolfgang who wouldn't bet any of his few remaining shiny new nickels on the prospect of selling these revolutionary analyses to the folks who run vegas. :) |
What's a boy to do?
When you chose the first, you had a 1/3 chance of being right, and nothing has changed that.
Scott, I assume you know what a Tontine is. Suppose you and two friends form one. Overlooking health and age differences and the fact that one smokes and drinks heavily, each of you has one chance in three of winning. Later, one of the others dies. Now, what is your chance of winning? vince Depends somewhat on your and their morality. There's a reason tontines were outlawed... Yeah, but I was presenting it as a question involving probabilities, not morality. (Or did you accidently omit the "t" from "mortality"? vince |
What's a boy to do?
When you first picked, you had a one in three chance of being right.
Right. With one board removed, your pick 'still' has a one in three (33 1/3 %) chance of being right. John, care to respond to my question, posted above? vince |
What's a boy to do?
"jeffc" wrote in message .. . "Wolfgang" wrote in message ... The question.......what should you do? The easiest way to convince yourself of the correct answer (since it's non-intuitive) is to play the game with someone. After a short while, you'll realize that the only way you can get it right if you don't switch is if you picked it right from the beginning - in other words, 1 chance in 3. Or just play by yourself: http://math.ucsd.edu/~crypto/Monty/monty.html This puzzle right smack dab in the center of my realm, as its a regular component of one of my classes. I can take you all to school on the solution on several levels, but I'm not working today so you're off the hook. MEANWHILE: how about this cherry; You toss three darts at a target. Dart A misses the target, then Dart B misses by even more. What is the probability that Dart C will miss by more than Dart A? --riverman |
What's a boy to do?
"riverman" wrote in message ... Or just play by yourself: http://math.ucsd.edu/~crypto/Monty/monty.html --riverman I got it right, 3 out of 5 times, by changing my selection each timed. Op |
What's a boy to do?
"Opus McDopus" wrote in message ... "riverman" wrote in message ... Or just play by yourself: http://math.ucsd.edu/~crypto/Monty/monty.html --riverman I got it right, 3 out of 5 times, by changing my selection each timed. Op Yep. A better way to convince yourself that changing doors is the best strategy is to make a spinner out of a paper clip and a piece of paper. Draw a circle divided in thirds, and unbend the paper clip so it works as a pointer, and hold it in the center with the pencil when you spin it. Agree beforehand that the prize is in a given section, and decide that you will always switch. After about three spins, it becomes abundantly obvious how it all works. --riverman |
What's a boy to do?
On Sat, 28 Oct 2006 20:55:19 -0400, vincent p. norris
wrote: When you chose the first, you had a 1/3 chance of being right, and nothing has changed that. Scott, I assume you know what a Tontine is. Suppose you and two friends form one. Overlooking health and age differences and the fact that one smokes and drinks heavily, each of you has one chance in three of winning. Later, one of the others dies. Now, what is your chance of winning? vince Depends somewhat on your and their morality. There's a reason tontines were outlawed... Yeah, but I was presenting it as a question involving probabilities, not morality. (Or did you accidently omit the "t" from "mortality"? If one of the tontine has none of the former, the other is apt to discover the quietness of the latter.... -- Antiquis temporibus, nati tibi similes in rupibus ventosissimis exponebantur ad necem. http://www.visi.com/~cyli |
What's a boy to do?
On Sun, 29 Oct 2006 11:02:22 +0800, "riverman"
wrote: Or just play by yourself: http://math.ucsd.edu/~crypto/Monty/monty.html This puzzle right smack dab in the center of my realm, as its a regular component of one of my classes. I can take you all to school on the solution on several levels, but I'm not working today so you're off the hook. Unfortunately, the first 4 or 5 times I tried it with not changing, I was right every time. Then the odds started to work out, but I had those early successes to work out of my mind. -- Antiquis temporibus, nati tibi similes in rupibus ventosissimis exponebantur ad necem. http://www.visi.com/~cyli |
What's a boy to do?
"vincent p. norris" wrote in message ... When you chose the first, you had a 1/3 chance of being right, and nothing has changed that. Scott, I assume you know what a Tontine is. Suppose you and two friends form one. Overlooking health and age differences and the fact that one smokes and drinks heavily, each of you has one chance in three of winning. Later, one of the others dies. Now, what is your chance of winning? vince If I'm one of the remaining members I'd say your chances were pretty damned good.... john |
What's a boy to do?
On Sat, 28 Oct 2006 06:35:31 GMT, "Bob Weinberger"
wrote: "Wolfgang" wrote in message oups.com... Actually, I believe your exactly right about the 2/3. :) Um.....well, it's been a couple hours since I last looked at the solution, so I could be wrong. :( The key is that the removal process is not random. Yep. Wolfgang Yes, the key from a pure mathematical probability standpoint is that the removal process is not random. Not as I see. As I see it, those supporting 50-50 odds aren't looking at the situation properly. I vaguely remembered the puzzle with Marilyn vos Savant, and of the explanations I saw, none really phrased the explanation both simply _and_ accurately (not that they aren't out there, I just didn't see them). Here's my explanation: Look at in reverse. Given the way Wolfgang phrased it, by switching, you essentially get to pick two boards. Let's change the phrasing such that if once you had picked board #1, he had given you the choice of sticking to that choice (1 chance in 3) or switching to pick _both_ of the two remaining boards (2 chances in 3), most people can easily see the odds advantage of switching and as such, would switch to picking two boards. You know one of the two will not and cannot have a five under it. At that point, Wolfgang turns one board of your two over and it's the one that isn't the five. He now offers you the choice of switching back to board #1. If you switch, you have traded your two-board pick back to Wolfgang for your original one board (1 chance in 3) pick. The fact that one board of your two-board (2 chances in 3) pick is now revealed is not material to the odds. You knew and expected that one of the two boards of your two-board choice couldn't and wouldn't have the five under it, so why would the fact that things are as you expected and as they have to be influence your new choice? This explanation is for the puzzle as Wolfgang explained, not all possible variants. For example, if a third person walks up at the point after the first board is turned over and is offered a chance to get in on things by picking one of the two remaining boards, their odds are 50-50, but they had different "rules" (this "each "hand's" _rules_ are different" is why blackjack ain't a heads-up game). And secondly, if you continue to play and Wolfgang is free to "change the rules" in every "game," the proper choice could change depending on what he does or doesn't do. TC, R |
What's a boy to do?
On 28 Oct 2006 14:35:06 -0500, basil ratbone wrote:
wrote in message .. . On Sat, 28 Oct 2006 00:24:58 -0400, "Tim J." wrote: typed: On Fri, 27 Oct 2006 23:39:09 -0400, "Tim J." wrote: typed: On Fri, 27 Oct 2006 22:43:52 -0400, "Tim J." wrote: Wolfgang typed: An interesting problem was recently brought to my attention. I like that one. Here's another less thought provoking oldie: We put you in a room and fill it with deaf people. Given the room is now quite crowded, we remove dead people, but add bad people. How many people are now in the room? That could be BAFfling... ... but wrong. How? deaf-dead = 2, 2 + bad = baf, no? May not be, but if not, ??? You never left the room. Um, you didn't say "we you in a room and _add_ deaf people..." Phrased the way you originally phrased it, wouldn't I be including in "deaf people?" I'm not a math geek, and I've never heard of this "oldie," I just thought it was more of logic thing with hex - f to d and back to f, but ??? I could understand it if it spelled something, but including me makes it bb0, no? Is that something hilarious to math prof-types or something? TC, R I would still knock you in the head and take your money along with the others. I would be the baddest person in the room. there would be a lot of dead people in the room . All those who woud remove them would also be dead. so , the answer is no one alive. I would leave with yours and theirs money. problem solved BASIL?!...BASIL?!...BASIL?!....you sound like a flowery ****... |
What's a boy to do?
"asadi" wrote in message ... If I'm one of the remaining members I'd say your chances were pretty damned good.... john Are we goin to remain on non-speaking terms forever? Op |
What's a boy to do?
wrote in message
Not as I see. As I see it, those supporting 50-50 odds aren't looking at the situation properly. For example, if a third person walks up at the point after the first board is turned over and is offered a chance to get in on things by picking one of the two remaining boards, their odds are 50-50, but they had different "rules" (this "each "hand's" _rules_ are different" is why blackjack ain't a heads-up game). As one who understands the mathematics, but still has difficulty rationalizing the counter-intuitive nature of the answer, I think this somewhat illuminates the crux. If the question is, "What is the probability of selecting the correct answer from two remaining random choices?", the answer is 1/2. That is the simplest and most understandable question. Everybody gets it. But that's not the actual question posed by the problem, nor are the choices random. The question posed is, "What is the probablity of selecting the correct answer through this process?" The correct answer to that is 2/3. Joe F. |
What's a boy to do?
On Sun, 29 Oct 2006 15:55:00 GMT, "rb608"
wrote: wrote in message Not as I see. As I see it, those supporting 50-50 odds aren't looking at the situation properly. For example, if a third person walks up at the point after the first board is turned over and is offered a chance to get in on things by picking one of the two remaining boards, their odds are 50-50, but they had different "rules" (this "each "hand's" _rules_ are different" is why blackjack ain't a heads-up game). As one who understands the mathematics, but still has difficulty rationalizing the counter-intuitive nature of the answer, I think this somewhat illuminates the crux. If the question is, "What is the probability of selecting the correct answer from two remaining random choices?", the answer is 1/2. That is the simplest and most understandable question. Everybody gets it. But that's not the actual question posed by the problem, nor are the choices random. The question posed is, "What is the probablity of selecting the correct answer through this process?" The correct answer to that is 2/3. I don't see how it's (objectively) counter-intuitive, and I think attempting to get too involved in "math" (beyond the basic) makes it more, rather than less difficult - for example, if it had been 4 boards, two were turned over revealing losers, and then the choice to change were given, to me, common sense indicates the odds say change your pick because of the same reasons I feel it does with 3. If you must have "math," I'm fairly sure the formula would be that the odds in favor of switching are pretty close to if not exactly x-1/x and the odds in favor of sticking are always exactly 1/x, when x is greater than 2, but I'm not a mathematician, so ??? Perhaps the odds in favor need to account for the first pick when x is higher than 3 - such that it isn't quite x-1/x - but it's always going to be better odds than 1/x. ****, that's confusing...that's why, IMO, algebra isn't the way to figure this out. About the only thing I can figure is that it is much like many threads on ROFF in that most folks, myself included at times, don't always _read_ what they are "reading," but rather, um, infer from what is written by what they _think_ is being said. In this case, they are simply ignoring that there are 3, not 2, boards and therefore, the chances cannot be 1 in 2. Heck, given the "game" as outlined by Wolfgang, there's nothing presented in the "rules" preventing the person from choosing the revealed losing board - they were simply offered a chance to change their pick. It would be the chooser making the obvious choice not to choose it because they can clearly see they won't win (they don't need to know that the chance of winning is 0 in 3). TC, R Joe F. |
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