# Bayes Rule Probability Problem

1. Mar 8, 2012

### Vendatte

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.