Conjunction fallacy I was reading this article which has the following question,

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?
Linda is a bank teller.
  Linda is a bank teller and is active in the
  feminist movement.

I chose the second option but according to a set theorem the choice was wrong. Why is not possible that linda can be both a bank teller and feminist? What is the simple explanation to this with example?
 A: Let $A$ be the event "she is active in the feminist movement" and let $B$ be the event "she is a bank teller."  Then "she is active in the feminist movement and is a bank teller" is $A\cap B$.  Whatever opinions one might have about whether bank tellers might or might not have a tendency to be active in the feminist movement, it is for certain true that $A\cap B \subseteq B$. Thus it is automatic that
$$P(A\cap B) \le P(B).$$
So we  cannot have $P(A\cap B) \gt P(B)$. It is logically impossible.  Information that we are provided  about Linda's background and history cannot alter that fact. 
A: I'm not sure if this answer is appropriate here, since it doesn't concern mathematics. It certainly concerns the question though.
This question is essentially a modified version of one given by Kahnemann and Tversky in a series of experiments. Even tough the probability that both A and B are true can never be higher than the probability of A alone, many test subjects violated this basic rule of probability. They commitet the conjunction fallacy.
The explanation of Kahnemann and Tverskywas based on people using a certain heuristic. People picture the situation described, and the easier it is to picture the situation, the more probable they consider the situation to be. Since the more extensive description paints a clearer picture, it gets associated with a more probable event. 
A: All the information about Linda's background is a complete red herring, intended to distract you into a wrong answer.
The simple fact is that as you add more constraints into a proposition, the circumstances in which that proposition is true can only decrease. More conjunction terms strengthen a proposition. They make it more specific.
This works across logic and set theory.
The intersection of sets A and B cannot be any larger than set A.
The stronger proposition P and Q cannot be true in more circumstances than the weaker proposition Q.
The number of women who are bank tellers and active in the feminist movement can be no larger than the number of women who are bank tellers (or the number who are active in the feminist movement).
A: Edit: because of a question merge, it should be clarified that the options A,B,C are referring to the propositions


*

*(A) It is more likely that "she is a feminist" than "she is a feminist and works in a bank"

*(B) It is less likely that ....

*(C) It is equally likely that ....
C can only be true if the chance of her being in an activist movement is 0% or the chance of her working in a bank is 100%.
B can only theoretically be true, if the chance of her working in the bank is more than 100%.
Edit: the previous answer was actually invalid (sorry!): C can only be true if the chance of her working in a bank is 100%.
