posted
I just came across an interesting trick question, which I shall share with you all. Suppose I tell you that Anna:
a) Is a female college student b) Majors in Women's Studies c) Is 21 years old d) Volunteers at the campus rape crisis center e) Often attends feminist rallies.
Now, which of the two following statements is more probably true?
1. Anna attends Harvard. 2. Anna is a radical feminist, and attends Harvard.
Posts: 10645 | Registered: Jul 2004
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posted
If 2 is true, then 1 is true too, right? Therefore 1 is definitely true, so it's the more probably true of the two.
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posted
Yeah, it'd be 1. They both contain the same condition, but the second one contains an additional condition.
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posted
Ah, I suppose that's correct. You didn't say that either one had to be true. However, I still think that 1 is more probably true, because it's true whenever 2 is true and in some other cases as well.
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But more accurately, I thought it interesting that most people (including myself for a few seconds until I re-thought) would answer wrongly.
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posted
Is there enough data there to answer that one? I know there are many more women truck drivers than women English professors at Ivy-league universities. What I don't know is what proportion of middle-aged female published English lit major poetry aficionados are professors vs how many are driving trucks. Truck driver still seems *more* likely, but only intuitively.
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posted
I don't understand what's interesting about this. Is there something beyond the obvious that I'm missing?
Posts: 37449 | Registered: May 1999
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posted
I'm with Dag -- what makes you think most people would answer 2? I din't find that "intuitive" for any fraction of a second.
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posted
I'm giving a lot of evidence that Anna is a feminist, but none that she attends Harvard. I think most people not trained in probability would therefore consider the question as being "Anna is or is not a feminist", rather than the choice actually presented. But my intuition about human behaviour could be wrong, of course. Why not try it out on some random victims and see what happens?
Posts: 10645 | Registered: Jul 2004
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quote:Originally posted by King of Men: I just came across an interesting trick question, which I shall share with you all. Suppose I tell you that Anna:
a) Is a female college student b) Majors in Women's Studies c) Is 21 years old d) Volunteers at the campus rape crisis center e) Often attends feminist rallies.
Now, which of the two following statements is more probably true?
1. Anna attends Harvard. 2. Anna is a radical feminist, and attends Harvard.
I'd answer 2. In fact, if you changed the options to this:
1. Anna attends Harvard. 2. Anna is a radical feminist.
quote:Originally posted by katharina: I've seen that, but I've seen it differently.
What if I told you that Anna:
a) Majored in English literature. b) Is 35 years old. c) Has had poetry published. d) Subscribes to American Poetry Review.
Now, which of the two following statements is more probably true?
1. Anna is an English professor at an Ivy-league university. 2. Anna is a truck driver.
I'd probably answer 1. I can't see why 2 would be at all more likely given the limited information available.
Posts: 12266 | Registered: Jul 2005
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quote:Originally posted by King of Men: I just came across an interesting trick question, which I shall share with you all. Suppose I tell you that Anna:
a) Is a female college student b) Majors in Women's Studies c) Is 21 years old d) Volunteers at the campus rape crisis center e) Often attends feminist rallies.
Now, which of the two following statements is more probably true?
1. Anna attends Harvard. 2. Anna is a radical feminist, and attends Harvard.
I'd answer 2. In fact, if you changed the options to this:
1. Anna attends Harvard. 2. Anna is a radical feminist.
I'd still answer 2.
And if I changed the options, your answer would be correct. As the question stands, though, your answer is not correct.
Posts: 10645 | Registered: Jul 2004
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quote:Originally posted by katharina: I've seen that, but I've seen it differently.
What if I told you that Anna:
a) Majored in English literature. b) Is 35 years old. c) Has had poetry published. d) Subscribes to American Poetry Review.
Now, which of the two following statements is more probably true?
1. Anna is an English professor at an Ivy-league university. 2. Anna is a truck driver.
I'd probably answer 1. I can't see why 2 would be at all more likely given the limited information available.
Well there are only 8 schools in the Ivy League. I just checked and Harvard has 16 women English professors. By extrapolation I'd estimate that there are only about 120 women English professors at Ivy League schools in the world.
In contrast, there are an estimate 3.2 million truck drivers in the US, about 5% of whom are women and about 30% of whom have some college education.
So as a rought estimate there are around 50,000 college educated women truck drivers in the US.
So given the limited information available, I think its far more likely that the woman is one of the ~50,000 college educated women truck drivers than one of the 120 Ivy league women English professors.
Posts: 12591 | Registered: Jan 2000
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quote:Originally posted by katharina: I've seen that, but I've seen it differently.
What if I told you that Anna:
a) Majored in English literature. b) Is 35 years old. c) Has had poetry published. d) Subscribes to American Poetry Review.
Now, which of the two following statements is more probably true?
1. Anna is an English professor at an Ivy-league university. 2. Anna is a truck driver.
I'd probably answer 1. I can't see why 2 would be at all more likely given the limited information available.
Well there are only 8 schools in the Ivy League. I just checked and Harvard has 16 women English professors. By extrapolation I'd estimate that there are only about 120 women English professors at Ivy League schools in the world.
In contrast, there are an estimate 3.2 million truck drivers in the US, about 5% of whom are women and about 30% of whom have some college education.
So as a rought estimate there are around 50,000 college educated women truck drivers in the US.
So given the limited information available, I think its far more likely that the woman is one of the ~50,000 college educated women truck drivers than one of the 120 Ivy league women English professors.
Can't she be both? Or am I just fantasizing?
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posted
I wrote a rather lengthy comment, but it was stupid and I can shorten it to: what is it about? What has intuition to do with it?
Posts: 723 | Registered: Dec 2004
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posted
I sat here for nearly five minutes trying to figure out why ANYONE would pick Option 2. It's self-evidently the less likely one, to the extent that I didn't understand what KoM was trying to say.
Then I had a thought: maybe, just maybe, people who don't think like programmers might have a problem with this. Because this question is actually about dependencies.
Let's break it down.
Given: Premise 1 supporting Claim B. Given: Premise 2 supporting Claim B. Given: Premise 3 supporting Claim B. Option 1: Claim A is true. Option 2: Claim A and Claim B are both true.
Someone who does not think in terms of nested dependencies might see this and observe that there is ample evidence for Claim B. A programmer, however, or anyone used to working with Boolean logic, perceives Option 2 instinctively as more restrictive than Option 1, since it requires an AND operator.
But I'm still surprised that anyone would pick Option 2, to be honest. It's completely foreign to my way of thought; I'm just speculating as to why it might happen.
(KoM, FWIW, I'm not convinced that most people would pick Option 2, but I'd be interested in seeing a survey.)
Posts: 37449 | Registered: May 1999
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posted
Well, so far we have Lisa and my wife picking option 2, several people stating that most others would do so, and a bunch of Hatrackers saying "It's obviously 1". Lisa would seem to contradict your programmer theory, which I admit I find surprising as well. As I say, go find some random victims and report your results. Posts: 10645 | Registered: Jul 2004
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posted
Incidentally, is anyone else seeing the Google ad for, I kid you not, "Feminist Blowjob Ringtone"? Posts: 10645 | Registered: Jul 2004
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posted
I think KOM's version of the question is certainly more obvious. Lisa's version is more subtle, and I think I might have guessed the English professor in that case. However, it does seem like the driver/Ivy professor problem is sort of like specificity in testing for rare diseases. Even if the test has 99% specificity, if the disease is rare enough, a majority of those who test positive would in fact not have the disease.
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posted
I avoided the other people's responses in this thread. I usually get these wrong but wouldn't 1 be more likely than 2 as 2 introduces an additional unknown rather than being simply different?
Posts: 14316 | Registered: Jul 2005
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posted
I'm not sure how this applies to intuition though. It seems more an analysis of a given set of parameters through personal experiences or beliefs. I guess subconsciously we always analyze something so at its core intuition could just be our subconscious analysis of a given set of facts...
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posted
I didn't like #2 because it still includes that pesky Harvard statement. If #1 was Anna goes to Harvard and #2 was Anna goes to Yale and is a radical feminist then what? It seems to me that then you have an unsupported statement and a unsupported statement combined with a supported one. Since the second one has some support, and the first none, the second is the better option. I bet a lot of people who answer number 2 are treating it that way.
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quote:Originally posted by Samprimary: #2 is the answer for blatant "stereotypes are a real time-saver" people.
I don't think so. #2 is simply the answer for those who don't understand what makes it less likely than #1. It's not unreasonable to assume Anna is a radical feminist on it's own. It's not stereotyping. It's not even insulting, really, unless you'd take being called a feminist as an insult or assume the more insulting use of the term "radical."* But that's a different discussion entirely.
*edit: or, I suppose, you find the term "radical" insulting when paired with "feminist" because you assume it implies that feminism itself is extreme and therefore crazy, unnecessary, etc.
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posted
I didn't find the options offered fit any of the notions that came to my mind. I'm not sure how it's been determined that "most people pick one of them, and they're wrong."
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posted
rivka: I think KoM was referring to "It seems to me that then you have an unsupported statement and a unsupported statement combined with a supported one. Since the second one has some support, and the first none, the second is the better option."
scholarette: no, it would still be more likely that #1 is true, if neither is required to be true. If one must be true, things get rather more complicated, but #1 would probably still be more likely (unless #1 was modified to be goes to harvard and is not a radical feminist).
Posts: 15770 | Registered: Dec 2001
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posted
I don't know why but this thread reminded me of an interesting blog post that I read awhile back on how people are more likely to believe a detailed prediction about the future than a general prediction about the future even though the extra detail necessarily makes the detailed prediction less likely. I wish I could find the link.
Posts: 1327 | Registered: Aug 2007
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quote:Originally posted by fugu13: rivka: I think KoM was referring to "It seems to me that then you have an unsupported statement and a unsupported statement combined with a supported one. Since the second one has some support, and the first none, the second is the better option."
posted
scholarette certainly seems to be asserting knowledge of something neither evident nor deductible.
Posts: 15770 | Registered: Dec 2001
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posted
Intuition is more commonly used to mean finding the right conclusion without a logical line of thinking to back it up, but there's a reason I used the language I did.
quote:A sense of something not evident or deducible; an impression.
posted
Well, if we're using it in that sense, then I agree that people's impressions are frequently incorrect. Posts: 32919 | Registered: Mar 2003
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quote:Originally posted by fugu13: rivka: I think KoM was referring to "It seems to me that then you have an unsupported statement and a unsupported statement combined with a supported one. Since the second one has some support, and the first none, the second is the better option."
scholarette: no, it would still be more likely that #1 is true, if neither is required to be true. If one must be true, things get rather more complicated, but #1 would probably still be more likely (unless #1 was modified to be goes to harvard and is not a radical feminist).
in my head, I added the requirement that the statement was all true or all false, which essentially means 1 is harvard and not feminist and 2 is yale and feminist.
Posts: 2223 | Registered: Mar 2008
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posted
If it must be all true or all false then if 1 is true(harvard), then 2 (yale) must be false and since I added all or nothing then the feminist part is false too. It was an extra rule I added which has no basis in the question.
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