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3. Suppose a patient may have a symptom (S) that can be caused by two different diseases (A and B). It is known that the variation of the G gene plays a major role in the emergence of disease A. Bayes Net and the corresponding conditional probability tables are shown below. For each section, you can leave your answer as an arithmetic expression. P(G) +g g 19 9 0.1 0.9 P(AG) +a +9 1.0 +g-a 0.0 0.1 a 0.9 +a G A S B +a +a +a +a a ·a a -a P(B) +6 0.4 -b 0.6 P(SIA, B) +b +s +b -S -b +s -b -S +b +s +6 -S -b +s -b -S 1.0 0.0 0.9 0.1 0.8 0.2 0.1 0.9
What is the probability that a patient has the disease carrying gene vanation G given that they have disease A? P(+g) + a) =
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