econ2040hw5 - KaitlynClune Econ2040HW5 11/8/10 1)

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Kaitlyn Clune Econ 2040 – HW 5 11/8/10 1) a) In order for the third student to be indifferent between guessing either  “red” or “blue”, the expected value of picking majority red would have to be  equal to the expected value of picking majority blue, based on the previous 2  choices.  By using Baye’s theorem:  Pr[majority red| red, red, blue] = Pr[majority red]x P[R,R,B| majority red]                 Pr[R, R, B] Where:  Pr[R,R,B] = Pr[majority blue] x Pr[R, R, B| majority blue] +    Pr[majority red]x  P[R,R,B| majority red]  = 1/9  Pr[majority red]x P[R,R,B| majority red] = ½ x (2/3)(2/3)(1/3) = ½ x 4/27 Thus: Pr[majority red| red, red, blue]  = (1/2)(4/27) / (1/9) = 2/3 If the total probability is 1, we know that Pr[majority blue| red, red, blue] = 1-(2/3) Thus Pr[majority blue| red, red, blue] = 1/3.  
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This note was uploaded on 11/11/2010 for the course ECON 2040 at Cornell University (Engineering School).

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econ2040hw5 - KaitlynClune Econ2040HW5 11/8/10 1)

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