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Server Time: 2/11/2012 2:42:29 PM PACIFIC |
 Monty Hall revisited, with a twist- survey also., Easy E, 19. May 2003 06:07 | ||
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| Don't want to bring this up again, but in the Sunday Parade magazine, someone wrote in about the Monty Hall/intuition "puzzle". He THEN said that one of his students posed this variation: Suppose I am taking a multiple-choice test. On one question, I randomly choose 1 of 3 answers. Then the instructor says that one of the remaining two choices is incorrect. Should I switch my choice? The "world's smartest woman" (or is that human? I forget what Marilyn vos Savant claims) said that the answer was: it doesn't matter. She did NOT, however, explain her reasoning. What am I missing here, because it seems like the exact same thing? Does it have to do with the way tests are scored, or that one wrong/right answer won't make a difference? Monty Hall Test survey a) Is this a correct statement? b) Or is the World's Smartest Woman not as smart as she thinks? Extra credit for detailed answers. | ||
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| Re: Monty Hall revisited, with a twist- survey also., shorn, 19. May 2003 06:18 | ||
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| She is wrong. You should switch because you are now given a 50% chance at winning while your original choice was only 33%. Not to mention that by revealing the fact that only one of the remaining two was wrong, you KNOW that your first choice was wrong. So, pick one of the other two and you increase your chances of winning by 17%. | ||
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| Re: Monty Hall revisited, with a twist- survey also., Easy E, 19. May 2003 08:04 | ||
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| on 19. May 2003 06:18 shorn wrote: > You should switch because you are now given a 50% chance at winning while your original choice was only 33%. Wait a minute- how is this NOT a 67% chance of the other choice being correct? Are you saying that this IS different than MH or not? >Not to mention that by revealing the fact > that only one of the remaining two was wrong, you KNOW that your first choice was wrong. huh? > So, pick one of the other two and you increase your chances of winning by 17%. Huh again? Why isn't it doubled? (see first part) | ||
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| Re: Monty Hall revisited, with a twist- survey also., shorn, 19. May 2003 08:28 | ||
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| Because all you know is that one of the other choices is wrong. Monty didn't tell you WHICH one it was like in the other example. So, you know that your first choice was wrong (because only one of the other two is wrong). So in this situation the second choice is an independent trial (because there was no chance your first choice was right). | ||
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| Re: Monty Hall revisited, with a twist- survey also., Easy E, 19. May 2003 09:47 | ||
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| on 19. May 2003 08:28 shorn wrote: > Because all you know is that one of the other choices is wrong. Monty didn't tell you WHICH one it was like in the other example. So, you know that your first choice was wrong (because only one of the other two is wrong). So in this situation the second choice is an independent > trial (because there was no chance your first choice was right). (just reread the post). AHHHHH... you read the statement "Then the instructor says that one of the remaining two choices is incorrect" as meaning that ONLY one of the remaining two choices was wrong.... I think that was a reach, if you would have thought about it, because then what would be the point of this post in the first place? Give me a LITTLE credit.... | ||
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| Re: Monty Hall revisited, with a twist- survey also., shorn, 19. May 2003 09:50 | ||
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| It reads "One of the remaining two". That would tell me, that the other one isn't, but maybe not. No matter what, in either scenarion you switch because you get better odds. | ||
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| Re: Monty Hall revisited, with a twist- survey also., stdioh, 20. May 2003 09:45 | ||
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| I think that the piece of information you are missing, shorn, is that she is not chosing what information to tell you based on what you picked. That is the crux of the matter. | ||
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| Re: Monty Hall revisited, with a twist- survey also., shorn, 20. May 2003 09:52 | ||
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| Well, we really don't know that is what she is doing because we don't get enough information. Either way, my initial choice still has only a 1/3 chance of being right, so it is a matter of getting 50% odds to switch or 66% depending upon how ytou interpret her message. | ||
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| Re: Monty Hall revisited, with a twist- survey also., stdioh, 20. May 2003 11:09 | ||
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| So the problem becomes either a 50:50 or a 33:67 depending on what she is actually doing. And we don't know what she is actually doing...so we need that information for sure or it is a bogus question. Nonetheless, we agree on what the odds are assuming that we know what the teachers intentions are and we should be able to leave it at that. | ||
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| Re: Monty Hall revisited, with a twist- survey also., shorn, 20. May 2003 11:17 | ||
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| yup... | ||
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| Re: Monty Hall revisited, corrected, Easy E, 19. May 2003 09:42 | ||
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| Sorry, my editing screwed this up (thanks for picking this up, shorn) Suppose I am taking a multiple-choice test. On one question, I randomly choose 1 of 3 answers. Then the instructor says that one of the remaining two choices is incorrect AND IDENTIFIES THE WRONG ONE. Should I switch my choice? | ||
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| Re: Monty Hall revisited, corrected, shorn, 19. May 2003 09:44 | ||
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| Under this scenario, it is the same as Monty Hall. Always switch because the third door has a 66 chance of being the right one. | ||
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| shorn, strangely enough, we may be wrong, Easy E, 19. May 2003 20:07 | ||
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| I still can't get my head wrapped around it, but my post on 2+2 in the Probability forum has generated some answers (and 5-1 against on the survey) that say that it's only a 50% chance in this scenario, since the instructor COULD have picked your answer to reveal (unlike Monty Hall, where he would know not to). As I said, I haven't gotten the ole' noggin around this yet. Just wanted to give you an FYI. | ||
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| Re: Monty Hall revisited, corrected, stdioh, 20. May 2003 09:47 | ||
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| If she chose a wrong one specifically for you based on your answer you would be right. Because she is telling the class, "this option is incorrect" then it makes no diffence. It is subtle, I know, but it matters if she is intentionally picking something that you didn't already pick or if there is a chance for her to identify the "door" that you already have as wrong. | ||
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| Re: Monty Hall revisited, with a twist- survey also., stdioh, 20. May 2003 09:44 | ||
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| Quite simply put, let us assume that one answer is distinctly right on the question all of the time. Now if the instructor picks a wrong answer to tell the class, it is not directly because of what the student chose. Money hall will always open a door other than the one you pick. The teacher will just pick a "random" wrong answer. Thus, you could already have it wrong and be told that your choice was wrong or have it right and have a wrong option eliminated. When that occurs, it says nothing for your initial choice. When you pick your fist choice (a) and are informed that (b) is incorrect, your axioms state that one of (a) and (c) is correct. Because (b) would be announced as wrong regardless of your innitial choice, you now have 50% to each remaining choice. If the teacher considered your response and then always told you that one of the other choices was wrong and pointed to either the other wrong one if you were wrong or one of the worng ones if you were right, then it would be isomorphic to the montey hall problem. | ||
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