Previous Calculation of Lung Cancer Yes = (0.5 * 0.1) + (0.5 * 0.01) = No = (0.5 * 0.9) + (0.5 * 0.99) = Calculation of Lung Cancer With evidence of Smoking Yes = (1 * 0.1) + (0 * 0.01) = 0.1 No = (1 * 0.9) + (0 * 0.99) = 0.9

Propagating Upwards Example of Has TB = yes What is Prob of Asia = Yes P(A= yes| H = Yes) = P(H = Yes| A = Yes) / P(H = Yes) = (0.05 * 0.01) / ((0.05 * 0.01) + (0.99 * 0.01)) =

A=YesA=No T=Yestpfp T=Nofntn The Reliability of the Tests becomes a probability itself

Probability of A Given Test One = True P(A = True| T = True) = c * P(T=True|A=True) * P(A=True) = c * 0.7 * 0.2 P(A = False| T= True) = c * P(T=True|A= False)* P(A=False) = c * 0.3 * 0.8 (c * 0.7 * 0.2) + (c * 0.3 * 0.8) = 1 c * ( ) = 1 c = 1 / 0.38 = P(A = True| T = True) = * 0.7 * 0.2 = P(A = False| T= True) = * 0.3 * 0.8 =

Probability of A Given Test One = True and Test Two = True P(A = True| T1 = True, T2 = True) = c * P(T1=True|A=True) * P(T2=True|A=True) * P(A=True) = c * 0.7 * 0.6 * 0.2 P(A = False| T1 = True, T2 = True) = c * P(T1=True|A=False) * P(T2=True|A=False) * P(A=False) = c * 0.3 * 0.1* 0.8 (c * 0.7 * 0.6 * 0.2) + (c * 0.3 * 0.1 * 0.8) = 1 c * ( ) = 1 c = 1 / = 9.26 P(A = True| T = True) = 9.26 * 0.7 * 0.6 * 0.2 = P(A = False| T= True) = 9.26 * 0.3 * 0.1 * 0.8 =