Student question

Recall the Linda example from class (one of the primary examples Tversky and Kahneman used to motivate the representativeness heuristic). Let us call the description of Linda given in the example simply "liberal." Suppose Mitch is a subject in the experiment, and he suffers from base-rate neglect as introduced in class: whenever he is thinking about whether a hypothesis is true, he acts as if the baseline probability (base rate) of the hypothesis being true is 50%. (For example, if he is thinking about whether Linda is a school teacher, he acts as if half the people are school teachers and half are not.) Mitch knows that a bank teller has a 15% chance of being liberal, while a person who is not a bank teller has a 50% chance of being liberal. Similarly, he knows that a feminist bank teller has a 75% chance of being liberal, while a person who is not a feminist bank teller has a 50% chance of being liberal.

(a) Derive the probability that Mitch attaches to Linda being a bank teller.

(b) Derive the probability that Mitch attaches to Linda being a feminist bank teller.

(c) Explain intuitively how the Linda example is a manifestation of base-rate neglect.