At some point, I'll have to see if I can find my copy of Professor Julius Sumner Miller's (http://en.wikipedia.org/wiki/Julius_Sumner_Miller) Enchanting Questions for Inquiring Minds. It's full of neat little problems with unexpected answers.
Example: Supposing you could fold a piece of paper in half 100 times, how thick would the result be?
Assuming standard 20lb paper? About 13 billion light years, assuming I haven't slipped a zero or two along the way - and if I have, well, you should still have a good idea of the scale we're talking. "A quarter of the visible universe" .
No, you're not missing any zeroes, that's basically it. Although at the time it was published (sometime in the 60s, I think), the answer was "bigger than the known universe".
I've asked a lot of people this one, and the standard intuitive answers range from metres to kilometres, with a few outliers guessing it would reach to the moon (which is at about the 42nd fold (http://www.wolframalpha.com/input/?i=%28thickness+of+copy+paper+*+2%5E42%29+%2F+distance+from+earth+to+moon)). I've only met a couple of scarily intelligent people who, without having heard it before, gave good ballpark estimates off the tops of their heads.
i'm always reminded of the story that has someone being paid in rice grains on a chessboard, starting with one and doubling each day ... gets big quickly
Depends what the right answer is, which is, naturally, the crux of the problem.
If we presume the right answer is "25%", then we have two chances of getting it right, but that means that random selection gives us a 50% chance of getting the right answer, and there's only one "50%" answer, with a 25% chance of randomly selecting it, so I have no idea. :)
The question doesn't indicate that there's only one correct answer, though -- it merely asks, "If you pick one, what are the odds that you'll be correct"? (It does imply that the answers one is choosing are from the list that follows, and that at least one of them is correct, though.)
I'm taking the phrasing of "If you chose an answer to THIS question" as being key. That specific question has 2 correct answers showing so the odds of picking the correct answer (B) is only 25%.
A, or D, but not both. In a multiple-choice exam, only one choice is actually the right answer, even when arguably two different answers could be argued to be equally correct. You ever prepped for the SAT or similar, you know this.
Except that isn't "two arguably different answers". That's the same answer, twice. Which means, in this case, that if it's the correct answer, it's the wrong answer, and if it's the wrong answer, it's the correct answer.
I've sat exams where it is allowed to select more than one response to a question. A proper exam will state the requirements of that exam. I see no reason to apply the rules to exams you've encountered to a single question stated without wider context.
I picked an answer at random. It was 60%. (It was random! It must be right! Hah!) But when I read the actual answers, it's like, oh, duh, 25%. Then it's like, wait, there are two 25%, so it must be 50%. But wait... I HATE YOU, PROBABILITY!
Depends who is grading the exam. I had a high school teacher once who used a holed out cover sheet that he would just place over the test. Made correcting the tests much faster. So in instances where I did not know the answer to a question I blotted out A, B, C, and D.
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(no subject)
Date: 2012-11-27 08:19 pm (UTC)Or am I remembering a different post with many entertainingly wrong answers?
Also, this sentence is false.
(no subject)
Date: 2012-11-27 08:23 pm (UTC)(no subject)
Date: 2012-11-27 09:00 pm (UTC)Example: Supposing you could fold a piece of paper in half 100 times, how thick would the result be?
(no subject)
Date: 2012-11-27 09:15 pm (UTC)Multiplication by two: It gets big, fast.
(no subject)
Date: 2012-11-27 10:05 pm (UTC)(no subject)
Date: 2012-11-27 10:23 pm (UTC)I think there was a schoolgirl who mathematically proved the maximum was 11.
(no subject)
Date: 2012-11-27 10:33 pm (UTC)(no subject)
Date: 2012-11-28 05:16 pm (UTC)(no subject)
Date: 2012-11-27 10:20 pm (UTC)I've asked a lot of people this one, and the standard intuitive answers range from metres to kilometres, with a few outliers guessing it would reach to the moon (which is at about the 42nd fold (http://www.wolframalpha.com/input/?i=%28thickness+of+copy+paper+*+2%5E42%29+%2F+distance+from+earth+to+moon)). I've only met a couple of scarily intelligent people who, without having heard it before, gave good ballpark estimates off the tops of their heads.
(no subject)
Date: 2012-11-27 10:27 pm (UTC)I was kinda surprised by HOW MANY light years once I did the math.
(no subject)
Date: 2012-11-28 12:20 pm (UTC)(no subject)
Date: 2012-11-27 08:33 pm (UTC)If we presume the right answer is "25%", then we have two chances of getting it right, but that means that random selection gives us a 50% chance of getting the right answer, and there's only one "50%" answer, with a 25% chance of randomly selecting it, so I have no idea. :)
(no subject)
Date: 2012-11-27 10:01 pm (UTC)You could go slightly mad with things like this though.
(no subject)
Date: 2012-11-27 10:07 pm (UTC)(no subject)
Date: 2012-11-27 11:39 pm (UTC)YMMV on being that focused on the wording though.
(no subject)
Date: 2012-11-28 12:36 am (UTC)(no subject)
Date: 2012-11-27 10:16 pm (UTC)if the correct answer is 25%, then your chance of reaching it by choosing an answer at random is 50% - meaning the correct answer is 50%, not 25%.
If the correct answer is 50%, then your chance of reaching it by choosing an answer at random is 25% - meaning the correct answer is 25%, not 50%.
(no subject)
Date: 2012-11-27 10:34 pm (UTC)(no subject)
Date: 2012-11-27 11:42 pm (UTC)In other questions, how many angels can dance on the head of a pin?
(no subject)
Date: 2012-11-27 11:41 pm (UTC)The odds of answering a generic question with those answers would be 25% and therefore 50%. But that question is phrased in a fairly specific way.
(no subject)
Date: 2012-11-28 12:35 am (UTC)Which would make the correct answer 25%.
And if the correct answer is 25%, the odds of picking that at random is 50%.
(no subject)
Date: 2012-11-28 01:22 am (UTC)(no subject)
Date: 2012-11-28 01:26 am (UTC)I love this question.
(no subject)
Date: 2012-11-27 08:37 pm (UTC)(no subject)
Date: 2012-11-28 12:52 pm (UTC)(no subject)
Date: 2012-11-28 12:38 am (UTC)(no subject)
Date: 2012-11-28 12:40 am (UTC)(no subject)
Date: 2012-11-28 02:37 am (UTC)(no subject)
Date: 2012-11-28 01:46 am (UTC)(no subject)
Date: 2012-11-28 01:54 am (UTC)(no subject)
Date: 2012-11-28 12:23 pm (UTC)(no subject)
Date: 2012-11-28 02:36 pm (UTC)(no subject)
Date: 2012-11-28 03:13 am (UTC)(no subject)
Date: 2012-11-28 03:22 am (UTC)(no subject)
Date: 2012-11-28 03:42 am (UTC)(no subject)
Date: 2012-11-28 03:50 am (UTC)Second: If that was an option, it would be wrong.
(no subject)
Date: 2012-11-29 03:09 am (UTC)(no subject)
Date: 2012-11-28 09:27 am (UTC)However, by adding 'E) 0%' as a fifth option you now have a 20% chance to select 0%, which then returns us to the original problem.
(no subject)
Date: 2012-11-28 05:11 am (UTC)(no subject)
Date: 2012-11-28 10:35 am (UTC)For instance, if my random method is to roll a fair d6 (1=A, 2-4=B, 5=C, 6=D) then B is correct for me.
(no subject)
Date: 2012-11-28 12:27 pm (UTC)(no subject)
Date: 2012-11-29 04:20 am (UTC)(no subject)
Date: 2012-11-28 05:40 pm (UTC)Got those questions correct every time.