6. Previous Calculation of Lung Cancer Yes = (0.5 * 0.1) + (0.5 * 0.01) = 0.055 No = (0.5 * 0.9) + (0.5 * 0.99) = 0.945 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

8. 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)) = 0.04807

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

15. 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 * (0.14 + 0.24) = 1 c = 1 / 0.38 = 2.631 P(A = True| T = True) = 2.631 * 0.7 * 0.2 = 0.3683 P(A = False| T= True) = 2.631 * 0.3 * 0.8 = 0.6314

16. 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 * (0.084 + 0.024) = 1 c = 1 / 0.108 = 9.26 P(A = True| T = True) = 9.26 * 0.7 * 0.6 * 0.2 = 0.7778 P(A = False| T= True) = 9.26 * 0.3 * 0.1 * 0.8 = 0.22224