Lecture11-ReasoningAndDecisionMaking-1.pptx

# Probhe 153 or 153 an application of bayes theorem

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Prob(H|E) = .153 or 15.3% An Application of Bayes’ Theorem Plug in the prior and conditional probabilities in Bayes’ equation to get the posterior probability of house being burglarized given evidence of door being ajar: 20

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Prob(H|E) = Prob(E|H) * Prob(H) Prob(E|H)*Prob(H) + Prob(E|~H)*Prob(~H) Prob(H|E) = (.5) * (.001) (.5)*(.001) + (.01)*(.999) Does this seem low to you? Prob(H|E) = .0477 or 4.8% An Application of Baye’s Theorem Plug in the prior and conditional probabilities in Bayes’ equation to get the posterior probability of house being burglarized given evidence of door being ajar: 21
Not really...People frequently underestimate the cumulative force of evidence and fail to take base rates into account in making probability judgments. Do people reason inductively in accordance with the model represented by Bayes’ Theorem? 22

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Kahneman & Tversky Evidence for Failure to Take Base Rates into Account 23
Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in politics or social issues and spends most of his free time on his many hobbies, which include home carpentry, sailing, and math puzzles. What is the probability that Jack is an engineer? Evidence for Failure to Take Base Rates into Account Participants in both groups gave a .90 probability estimate to the hypothesis that Jack is an engineer. 24

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Bill is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. What is the probability that Bill is an engineer? Evidence for Failure to Take Base Rates into Account Participants in both groups gave a .50 probability estimate to the hypothesis that Bill is an engineer. 25
Framing Effects In cases where there is not a clear basis for making a decision, people are influenced by the way the problem is framed . 26

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Problem 1: Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows: If Program A is adopted 200 people will be saved. If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-thirds probability that no people will be saved. Which of the two programs would you favor? Asian Disease Crisis 27
Problem 2: Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows: If Program C is adopted 400 people will die.

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