Tversky and Kahneman23 asked a group of subjects to carry out the following task. They are told that: Linda is 31, single, outspoken, and very bright. She majored in philosophy in college. As a student, she was deeply concerned with racial discrimination and other social issues, and participated in anti-nuclear demonstrations. The subjects are then asked to rank the likelihood of various alternatives, such as:
(1) Linda is active in the feminist movement.
(2) Linda is a bank teller.
(3) Linda is a bank teller and active in the feminist movement. Tversky and Kahneman found that between 85 and 90 percent of the subjects rated alternative (1) most likely, but alternative (3) more likely than alternative (2). Is it? They call this phenomenon the conjunction fallacy, and note that it appears to be unaffected by prior training in probability or statistics.
Explain why this is a fallacy. Can you give a possible explanation for the subjects’ choices?

B = Throughout the feminist movement, Linda is active. Because alternative (3) is "A" and "B," it's indeed lower than the alternative (2) corresponding to "B" ( event "A and B" is a subset of event "B").

In option A or substitute is [tex](A \cap B) \sqsubseteq A[/tex], i.e. [tex]P(A \cap B) \leq P(A)[/tex]. Therefore, A is much more likely [tex](A \cap B)[/tex]. It is, therefore, a greater probability of option (2)and (3).