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1. Bayes Network. lncidenoes of diseases A and B (D A, D B) depend on the exposure (E). Disease A is additionally inuenced by risk factors (R). Both diseases lead to symptoms (5'). Results of the test for disease A (TA) are affected also by disease B. Positive test will be denoted as TA = 1, negative as TA = 0. The Bayes Network is shown in Figure 1. Needed conditional probabilities are shown in Table 1. 9 Q @0 Figure 1: The DAG of the Bayesian networks Table 1: The known (or elicited) conditional probabilities E 0 1 R 0 1 0.8 0.2 0.7 0.3 Dij 0.95 0.05 DchB 0.92 0.08 DEDB 0.5 0.4 BEDS 0.8 0.2 DAD'B 0.4 0.6 DADCB 0.15 0.85 DADB 0.1 0.9 DADB 0.03 0.97 (a) What is the probability of disease A (D A = 1), if disease B is not present (DB = 0), but symptoms are present (5' = 1). (b) What is the probability of exposure (E = 1), if symptoms are present (5' = 1) and test is positive (TA = 1)