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Q3. (a) (Beliefs) (This question is related to the famous \"Linda.\" experi ment by Kahneman and Tversky and the corresponding \"conjunction fallacy\"). Suppose we have picked a person at random, and nd that her name is Linda Subjects and obtain some background information about her.1. There are two 1This information is not relevant for what follows, but just so you know the subjects are dimensions of uncertainty about Linda: her job, and her ideology. To keep things simple suppose the dimensions are described by just the following 8'1 = {bank teller, not a, bank teller} 32 = {feministmot a, feminist}. Use the notation 31 = {la-lb} and 32 = { f, . f } Based on this background information, subjects in experiments form likelihood judgements 333 over the state space S = 51 x 8'2. (i) Write out the state space. (ii) Write down each of the following two events as subsets of the state space: \"Linda is a bankteller\" and \"Linda is a feminist bankteller\". (iii) Subjects in experiments often say that \"it is more likely that Linda is a feminist bankteller than she is just a bank teller\". Prove that these likelihood judgements cannot be described by a probability measure over S