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Bayes Rule Probability Problem

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Event B is cow has BSE
    Event T is the test for BSE is positive
    P(B) = 1.3*10^-5
    P(T|B) = .70
    probability that the test is positive, given that the cow has BSE
    P(T|Bcc) = .10
    probability that the test is positive given that the cow does not have BSE
    Find P(B|T) and P(B|Tc)
    probability that the cow has BSE given that the test is positive, and probability that the cow has BSE given that the test is negative

    2. Relevant equations

    P(Ci|A) = P(A|Ci)/P(A) = P(A|Ci) / (P(A|C1)P(C1)+P(A|C2)*P(C2) ... + P(A|Cm)*P(Cm)


    3. The attempt at a solution

    The equation I use to find P(B|T) is

    P(B|T) = P(T|B) / (P(T|B)*P(B)+P(T|BC)*P(Bc)

    plugging in the values, I get P(B|T) = .70/(.70*(1.3*10^-5) + .1(1-(1.3*10^-5))), however that value is close to 7, which is clearly wrong.

    To find P(B|Tc I plan on using the equation P(B) = P(B|T)P(T)+P(B|Tc)*P(Tc)

    Any help would be greatly appreciated.
     
  2. jcsd
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