Following up, I’m going to hazard a psychological explanation of the conjunction fallacy. When presented the choices, “(1) Linda is a bank teller (2) Linda is a bank teller and is active in the feminist movement”, here is what I think happens in the subject’s mind. Upon encountering (2), I conjecture that the subject re-interprets (1) as “Linda is a bank teller and not active in the feminist movement”. There must be some clever experiment to verify this empirically. If this is what’s actually happening, then whatever is faulty is not the probabilistic reasoning. Of the two (new) conjunctions, (2) could indeed well be more probable.
I suspect that untrained people’s poor performance in probability stems from a more basic incompetence in logic. Ask a random adult, “What’s the opposite of ‘always’?” I’ll bet most people will blurt out, “Never”. Now there’s the issue of how one interprets opposite, which I take to mean logical negation. In that case, the correct answer is not always rather than never. Setting this up as a clean experiment is a bit of a challenge. Using my wording with “opposite” invites criticism on the grounds of ambiguity. Using the more precise “logical negation” might be judged as technical and arcane. If anyone can phrase the question in a way that’s both natural and unambiguous, I’d be curious to know.