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In a court, a junior (she) is assigned  the role to determine whether a criminal defendant (he) is innocent (I) or quilty (G).

The record of past cases suggests that he is innocent with probability 20% and guilty with probability 80%, i.e., Pr(I)=0.2; Pr(G) (they are called prior probabilities)

If he truly innocent, the evidence of his innocence (I) will be submitted to the court with probability 60%, and the evidence of guilty (g) will be with probability 40%; i.e., Pr(I|G)=0.3

1) Derive the probability that she receives the evidence of innocence; i.e. Pr(I)

2) Derive the probability that she receives the evidence of guilty; i.e., Pr(g).

3) If she receives the evidence of his innocence, what is the conditional probability of his innocence; i.e., Pr(I|i)? Also, what is the conditional probability of his guilty; i.e., Pr(G|i)?

4) If she receives the evidence of his guilty, what is the probability of his innocence, i.e., Pr(I|g)? Also, what is the conditional probability f his guilty; i.e., Pr( G|g)?

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