1. (10 p) Consider the following Bayesian network with the random variables: pol

Question

1. (10 p) Consider the following Bayesian network with the random variables: politically Motivated prosecutor B Broke election law, I- Indicted, M G = found Guilty, J = Jailed. B M P(I) 5 P(B) P(A .0 G PJ 0 (a) Determine the probability that someone broke the election law, was indicted, found guilty, and went to jai, and the prosecutor was not politically motivated. First express its formula in symbolic form. Then express the formula in numeric form and calculate it. (b) Determine the probability that someone goes to jail given that he broke the law, has been indictec and faces a politically motivated prosecutor. First express the formulas in symbolic form, and then calculate them. You may try to find a solution that does not involve many computations.

Explanation / Answer

Ans:(a)The probability depends upon P(B,G,I,M,J) = P(B) P(G|I) P(G|B) P(M|I,J) P(J/B,I)

=0.9*0.9*0.1*0.9*0.9=0.065

(b)Probability=P(G|B,I,M)=1-(1-fGB)(1-fGI)(1-fGM)

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