24 July 2011

Which is more probable?

"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 of the following two alternatives is more probable?
1. Linda is a bank teller.
2. Linda is a bank teller and active in the feminist movement.

The answer is in the Futility Closet.


  1. Interesting that the question itself is a linguist mess. It's probable that the writer is not an English major or is a graduate of an American university.

  2. Seen this question before. Very interesting. The answer is, of course, the first one.

  3. I think you meant to say "a linguistic mess."

  4. Linguistic? Yes, why didn't I see that?

  5. This is too easy. The probability of having one attribute is always greater than the probability of having that same attribute plus another attribute. Being a feminist in this context seems likelier than bank teller, but that's a red herring. Probability of A will always be greater than or equal to A union B.

    This becomes much more clear if you make A = "feminist". Becomes pretty clear that if you add B = "bank teller" to the mix you cut the odds.

  6. Most people probably assume extra details such that 1) becomes: Linda is a bank teller and not a feminist.

    I'm curious what would happen if they actually gave enough information in the question to answer logically without having to make the association between Linda's stated attributes and feminism.
    Would that then trip the logic mode flags in our brains so we'd see the trick more readily?

  7. Actually, neither answer is likely. Banks do not like to hire very bright people as tellers, for fear they will be able to more easily figure out how to successfully steal money.

  8. I was about to say that you didn't even have to tell Linda's story to answer that question ... but then I read Kay's comment and had to stop and laugh!

  9. I believe the purpose of telling Linda's story is to mislead people into choosing the second option. Without the story the answer is blindingly obvious.

    I've subsequently tried this trick on people, substituing the choices of "A Republican" and "A Republican who watches FOX News." With the proper description of the person as an extreme conservative, people ignore the math and opt for the second choice.

  10. Odd - when I read it my first thought was "There's no relevant information, how can I say".

  11. The question itself is flawed. It says "alternative" suggesting that the answers are mutually exclusive. The second answer has explicit detail, which, by implication, the first answer appears to negate because it doesn't offer an alternative.

    I think the study is trying to find prejudice where there may be none.

  12. Look at Gigerenzer's take on it. This problem shows that humans showcase context sensitive reasoning. The story presented in the question lets the reader assume it has to be relevant to the question at order. Also polysemantics can account for confusion. http://en.wikipedia.org/wiki/Conjunction_fallacy

  13. I cannot bring myself to believe that people get probability this wrong. It has to be the case that the error is made because people assume that, since there is a choice, the first option implies that she is not a feminist.

  14. Squibfish:

    That probably does happen to a lot of people reading that, although I think it would still be wrong if the first said "and NOT [active feminist]". Most 31-year-olds are not active in movements related to the signs they were holding in college.

    Also, look at Note 2 on the Wikipedia page from thms' post. Clarifying does not help. They still chose the wrong answer even with clarification.

    I think the real cause is not that people "get the probability wrong", but that they don't really even do the probability. Instead of thinking in formulas and charts (not even simple ones), they just go with whichever answer tickles their intuitions the most.

    Though Gigerenzer thinks it is a grammer issue, his experiment not only words it clearly, but also provides a worksheet-style format which forces people to lay down numbers in a rational way. Given that Tversky's and Kahneman's explicit form of the question did not change the results, but Gigerenzer's explicit question with guided logic DID change the results, I think the second thing is the issue.



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