# Explain intuitively why the odds ratio in () does not depend on Pr (pocket protector j Jack is an engineer).

1. (30 points) Match each of the stories below with at least one of the following phenomena: availability bias base-rate neglect con?rmation bias conjunction fallacy disjunction fallacy and explain brie?y what the bias entails and why it ?ts the story.
(a) (6 points) Claire?s car is old and has not been well-maintained. Her friend who is an experienced car mechanic warns her that there is 5 per cent probability of breaking down every kilometre. Claire really wants to visit her mother in the nursing home that is about twenty kilometres away. Pondering her friend?s warning that the car has a 5 per cent probability of breaking down each kilometre she ?gures that the probability of breaking down during the trip cannot be much higher than ?fteen per cent. She is shocked when her car breaks down half way to the nursing home.
(b) (6 points) Denise lost all her luggage the last time he checked it in. She vows never again to check her luggage in even if it means having unpleasant arguments with fl?ight attendants.
(c) (6 points) Although having never travelled outside the ACT Clarence gets him-self tested for malaria. The test comes back positive. Convinced he will die of malaria he asks his his priest to perform the Viaticum or Last Rites.
(d) (6 points) Doug has always been convinced that people of Roma (gyspy) descent are prone to thievery. Several of his co-workers have a Roma background and he knows they are not thieves. One day a friend shares a story about two people who looked like gypsies?stealing goods from a grocery store. ?I knew it!?Doug says to himself.
(e) (6 points) Lena does not think it is likely that Greece will leave the Euro-zone and start issuing again its own currency the Drachma. She does think it is quite likely that the UK will vote to leave the European Union in the upcoming referendum that PM David Cameron has promised to hold before 2017. However when asked what she thinks about the possibility that Greece will leave the Euro-zone and the UK will vote to leave the European Union she thinks that is more likely than the possibility that Greece leaves the Euro-zone.
2. (30 points) Consider the following experiment that Kahneman and Tversky ran to study base-rate neglect. In Problem A subjects are told that Jack has been drawn from a population of 30% engineers amd 70% lawyers and that Jack wears a pocket protector.
(a) (5 points) Let pA denote the probability that Jack is an engineer given that he wears a pocket protector. Using Bayes?rule show that the odds that Jack is an engineer as opposed to a lawyer are given by:
pA
1 ? pA
= Pr (pocket protectorj Jack is an engineer)
Pr (pocket protector j Jack is a lawyer)
0:3
0:7
In Problem B subjects are told that Jack has been drawn from a population of 70% engineers and 30% lawyers and that Jack wears a pocket protector.
(b) (5 points) Let pB denote the probability that Jack is an engineer given that he wears a pocket protector. Show that: pB
1 ? pB = Pr (pocket protectorj Jack is an engineer)
Pr (pocket protector j Jack is a lawyer)
0:7
0:3
And conclude that if subjects form beliefs according to the laws of probability it must be the case that:
pA= (1 ? pA)
pB= (1 ? pB)
= 9
49
. ()
(c) (5 points) Explain intuitively why the odds ratio in () does not depend on Pr (pocket protector j Jack is an engineer).
(d) (5 points) Explain why Kahneman and Tversky set up the experiment in this way.
(e) (5 points) What values of pA= (1 ? pA)
pB= (1 ? pB) imply that subjects exhibit base-rate neglect?
(f) (5 points) Kahneman and Tversky ran this experiment as a between-subjects
design ?dierent groups of subjects responded to Problems A and B. How might their results have changed if they had run a within-subjects design ?where each subject responded to both problems? Why do you think Kahneman and Tversky chose a between-subjects design.
3. (40 points) Anna is an investor who observes two quarters of performance by Bruce a mutual-fund manager. Each quarter Bruce has probability p of beating the market and probability 1 ? p of failing to beat the market. The probability p is either 0 1=2 or 1 depending on whether Bruce is respectively a bad mediocre or good fund manager. Bruce?s performance is independent from one quarter to the next. Hence Bruce?s performance can be modelled correctly as draws with replacement from an urn with 2 balls where a proportion p of the balls corresponds to good performance and a proportion 1?p of the balls correspond to bad performance. Anna however incorrectly ?thinks ?the balls are being drawn without replacement.
(a) (10 points) Identify which heuristic this model is intended to capture and describe this heuristic in one sentence.
(b) (5 points) Suppose for now that Anna knows for sure that p = 1=2 (that is Bruce is a mediocre fund manager) and she has just observed one good quarter?s performance by Bruce. What is her prediction about Bruce?s performance in the next quarter? Explain your answer.
(c) (15 points) Suppose now that Anna doesn?t know p except that it can be either 0 1=2 or 1 and it is equally likely to be any one of those three values. What does she conclude if she sees: (i) two good performances by Brian? (ii) two bad performances by Brian? (iii) one good and one bad quarter of performance? Are these conclusions correct? Explain the reasoning behind your answer.
(d) (10 points) Explain how the prediction of this model in part (c) (i) is related to the hot-hand fallacy in basketball.

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