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econ2040hw5

econ2040hw5 - KaitlynClune Econ2040HW5 1 a) redorblue,...

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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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econ2040hw5 - KaitlynClune Econ2040HW5 1 a) redorblue,...

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