Please answer with the first choice that came to mind, 1 or 2 (but please don't include your reasoning for now). - Stephen Mack #TeamMomo

2 - RudĩϐЯaЯïan

1 - Todd Hoff

Cristo changed his answer. - Akiva

^____^ - Akiva

1 - Tamara

1 - imabonehead from Android

Bump. Any other folks want to answer? - Stephen Mack #TeamMomo

1. - Louis Gray

1. - Anika

Last bump before commentary! - Stephen Mack #TeamMomo from iPhone

1 - Fish Are LIES

2. - Mary B: #TeamMonique

2 - Eric

2 - Jonathan Disher

2 - Georgia from iPhone

2 - LB: #TeamMonique

OK, so I learned about this one today and my answer was 2 as well. But that's wrong. Presuming that everyone agrees from the information that's provided that the chance of Bob being a Democrat isn't 100% (even if we estimate it at a high value, such as 90%), then 1 is a more probable statement than 2. Since both answers have the idea of Bob being a teacher, that portion is equally probable. Statement 2 requires both that Bob is a teacher and that he's a Democrat. "And" statements must multiply their probabilities to be true. So if you have a statement like "Bob is going to flip heads and then flip tails," that statement's probability of being true is 25% (0.5 x 0.5), whereas "Bob is going to flip heads" has a 50% probability. This is apparently called the Conjunction Fallacy, but http://en.wikipedia.org/wiki... points out that it may be a defect of how the question is asked rather than a thinking error. I saw that Todd Hoff explained this properly when he first answered (before I edited my first comment to say not to include reasoning). I encountered this question in a Quora article (http://www.quora.com/What-ar...) posted by Adriano (http://friendfeed.com/cogsci...). - Stephen Mack #TeamMomo

I was going to say 1, just going by pure logic. One thing would always be more probable than two things, wouldn't it, as long as both things are reasonable. - Jandy

Has to be 1. Even if 99.999999% of teachers are democrats, then the set of democrat teachers will be smaller than the set of teachers. Ergo. QED. And all that. - Yo. Shark Dog.

^ That, too. - Jandy

Are you looking to be least wrong or most right? Because 1 works for the former and 2 for the latter. - Heather

Heather, I think you're right that that exposes some weakness in the fallacy. In a strictly logical sense, "A *and* B" is always less probable than "A" because the entire statement is either true or false and we must evaluate the probability of the entire statement. But in ordinary usage, we tend to evaluate statements by how much truth is in them, and answer 2 seems to have a higher probability of having at least one true statement. - Stephen Mack #TeamMomo

But he lives in California where all teachers are Democrats with LIBERAL arts degree's ;-) - Eric

1 was (to me) obviously the right answer. Why isn't this obvious? Is there a different interpretation of the question other than the one coming from elementary probability theory? "A" is obviously more probable than "A and B" if the probability of B is less than 1. Maybe it has something to do with me learning English as a second language and having a scientific / mathematical education background, but I see no doubt and no potential for confusion here. - Tudor Bosman

Lesser known fact: Bob protested the Conjunction falacy. - Micah from FFHound(roid)!

Tudor, as phrased with the "more probable" wording, you're right. But many people look at 1 and say, "Hmm, maybe but probably not" and then look at 2 and see the Democrat portion and think, "Well, it's at least half right." - Stephen Mack #TeamMomo

Jandy and Just Joe, yes, both of you expressed your reasoning well. Tudor too. I agree with you after the fact (but I still got it wrong when I didn't think it through properly). And ha ha to Eric and Micah. :) - Stephen Mack #TeamMomo

Stephen: It would be interesting to see how this plays out when you consider people's biases. Do a blind test: tell the same story to a group of people, and ask half of them if they'd agree with the statement "Bob is a teacher" and the other half if they'd agree with the statement "Bob is a teacher and a Democrat." I bet more people will agree with the second statement than with the first. - Tudor Bosman

Daniel Kahneman won his Nobel prize studying such heuristic flaws in intuitive thinking: http://edge.org/convers... -- so it's not uncommon :-) - Adriano

1 - Jimminy IS Everybody

2 - of course this was before I read the rest of the thread. :/ - #cryptic

P(A∩B) is always ≤ P(A) but those preceding statements will probably affect your pre-test probability :D - Victor Ganata

Adriano: that is an excellent read. - Tudor Bosman

Somehow I think this should be related to Occam's Razor/The Law of Parsimony somehow. - Victor Ganata

1 - Ruchira S. Datta

From the article that Adriano linked: "Probability is hard, similarity is immediate" -- I agree with Tudor, excellent read. - Stephen Mack #TeamMomo

1 - Kevin Fox

I think that if human beings had an intuitive grasp of probability, Las Vegas wouldn't exist. - Victor Ganata

Wouldn't greed still be the stronger force? - Todd Hoff

There are higher probability ways of (at least temporarily) satisfying greed. :) - Victor Ganata

But not as directly rewarding. Gambling is hacking the dopamine system, so your logical arguments have a low probability of being successful :-) - Todd Hoff

Even if we shift to talking about the dopamine reward circuit, I still think that if probability were intuitive, there'd be more drug users and fewer gamblers ;) - Victor Ganata from iPhone

We seem to have plenty of both. - Todd Hoff

Dopamine. The cause of, and the solution to, all of life's problems. - Victor Ganata

2. Bob is a teacher and a Democrat. - Bubba was a rollin stone

3. Bob is boring - Mo Kargas

Victor: For some of us, gaming (in my case, video poker) is interesting cheap entertainment, and the actual odds keep it pretty cheap. Might not be true for most casino-goers. - Walt Crawford

Kahneman's classic version (a bit dated now): "Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable? 1) Linda is a bank teller. 2) Linda is a bank teller and is active in the feminist movement." And Stephen J. Gould's comment on it: "I am particularly fond of this example [the Linda problem] because I know that the [conjoint] statement is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me—“but she can’t just be a bank teller; read the description.”" - Eivind