Bays rule
P(A|B) = P(B(A))P(A)/P(B)
P(¬A|B) = P(B|¬A)P(¬A)/P(B)
P(A|B)+P(¬A|B) = 1
P'(A|B) = P(B|A)P(A)
P'(¬A|B) = P(B|¬A)P(¬A)
P(C)=0.01
P(+|c)=0.9
P(-|+c)=0.8
P(¬C)=0.99
P(-|C)=0.1
P(+|+C)=0.2
Conditionally Independent
P(T2|C1 T1) = P(T2|C)
P(T2 =+1 | T1 =t)
= P(+2 | +1 ,C) P(C|+1)+P(+2|+,¬C)P(¬C|+1)
= P(+2|C)*0.043 + P(+2|¬C)*0.957
= 0.2301
