Susan 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-nuke demonstrations.You were asked to rank the probabilities of certain things about Susan. Two of the choices were
a bank teller
a bank teller and an active feminist
LOGICALLY bank teller and feminist would have a HIGHER probability than bank teller and and active feminist. Some people (including me when I first was given this exercise) ranked bank teller lower bank teller and active feminist. Why? I think that either people are not good at logic in real-world situations or people implicitly view bank teller as bank teller and NOT an active feminist. This problem has been extensively studied and there are other opinions.
Of the 30 responses I got before posting this roughly 10 ranked bank teller higher than bank teller and and active feminist (which is correct), 10 ranked bank teller and and active feminist higher than bank teller, and 10 of the answers were not relevant (e.g., clarifications of the question). (One person I blocked since he explained the above and would have given away the game, and one person who left a comment 5 minutes ago I will let through but only after I post this.)
I recommend giving this exercise to students in a class that covers logic and/or probability to see what they say.
Clyde Kruskal told me about this problem. He found it here though its also at other sites. This source credits the following (which I would guess is correct). Tversky, Amos; & Kahneman, Daniel (1983), Extensional Versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment", Psychological Review 90(4) (October): 293-315. They are famous for these sorts of psychology questions. The latter won the Nobel prize in economics for joint work with the former.
The notion that A is less likely than A AND B is called The Conjunction Fallacy. The article pointed to only gives the two choices: (1) Bank Teller, and (2) Bank Teller and an active feminist. I think its better to give all of those choices as is done here other presentations of this exercise.