The government of Ghana has decided to automate the analysis of judged cases to flag out poorly judged cases and to determine whether the cases processed at the law courts were fairly attended to or not. An artificial Intelligent software using Bayesian filter is to be used to measure the intelligence in processing legal cases to determine whether a judgement made by judges are fair or not. A set of cases were fed into the memory of the software for processing the cases and determining fairness in the cases. The elements of the cases presented were the evidences gathered and the judgement made. The filter is to determine following probabilities: P (J)=probability that there was a judgement on the case and the judgement was fair. P (J') = probability that there was a judgement orn the case and the judgement was not fair. P (E)= probability that there were evidences and the evidences were valid. P (E') = probability that there were evidences and the evidences were not valid. Let P (J) =0.85 be probability that there was a judgement on the case and the judgement was fair. Let P(E/J) =0.13 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were fair. Let P (E/J') =0.82 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were not fair. Assuming you are part of the research team that induces the intelligence into the machine, solve the following questions below. 1. Draw the,Bayesian Network diagram in a form of a tree diagram to form the basis of reasoning for the machine for the above situation 2. Calculate for the probability that there was a judgement on the case and the judgement was not fair P (J') 3. What is the probability of non-valid evidences based on the condition that there were judgements on the case and the judgement were not fair P(E'/J')?
The government of Ghana has decided to automate the analysis of judged cases to flag out poorly judged cases and to determine whether the cases processed at the law courts were fairly attended to or not. An artificial Intelligent software using Bayesian filter is to be used to measure the intelligence in processing legal cases to determine whether a judgement made by judges are fair or not. A set of cases were fed into the memory of the software for processing the cases and determining fairness in the cases. The elements of the cases presented were the evidences gathered and the judgement made. The filter is to determine following probabilities: P (J)=probability that there was a judgement on the case and the judgement was fair. P (J') = probability that there was a judgement orn the case and the judgement was not fair. P (E)= probability that there were evidences and the evidences were valid. P (E') = probability that there were evidences and the evidences were not valid. Let P (J) =0.85 be probability that there was a judgement on the case and the judgement was fair. Let P(E/J) =0.13 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were fair. Let P (E/J') =0.82 be the probability of valid evidences based on the condition that there were judgements on the case and the judgement were not fair. Assuming you are part of the research team that induces the intelligence into the machine, solve the following questions below. 1. Draw the,Bayesian Network diagram in a form of a tree diagram to form the basis of reasoning for the machine for the above situation 2. Calculate for the probability that there was a judgement on the case and the judgement was not fair P (J') 3. What is the probability of non-valid evidences based on the condition that there were judgements on the case and the judgement were not fair P(E'/J')?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:The government of Ghana has decided to automate the analysis of judged cases to flag out poorly
judged cases and to determine whether the cases processed at the law courts were fairly attended
to or not. An artificial Intelligent software using Bayesian filter is to be used to measure the
intelligence in processing legal cases to determine whether a judgement made by judges are fair
or not. A set of cases were fed into the memory of the software for processing the cases and
determining fairness in the cases. The elements of the cases presented were the evidences gathered
and the judgement made. The filter is to determine following probabilities:
P (J)=probability that there was a judgement on the case and the judgement was fair.
P (J') = probability that there was a judgement orn the case and the judgement was not fair.
P (E)= probability that there were evidences and the evidences were valid.
P (E')= probability that there were evidences and the evidences were not valid.
Let P (J) =0.85 be probability that there was a judgement on the case and the judgement was fair.
Let P(E/J) =0.13 be the probability of valid evidences based on the condition that there were
judgements on the case and the judgement were fair.
Let P (E/J') =0.82 be the probability of valid evidences based on the condition that there were
judgements on the case and the judgement were not fair.
Assuming you are part of the research team that induces the intelligence into the machine, solve
the following questions below.
1. Draw the, Bayesian Network diagram in a form of a tree diagram to form the basis of
reasoning for the machine for the above situation
2. Calculate for the probability that there was a judgement on the case and the judgement was
not fair P (J')
3. What is the probability of non-valid evidences based on the condition that there were
judgements on the case and the judgement were not fair P(E'/J')?
4. What is the probability of non-valid evidences based on the condition that there were
judgements on the case and the judgement were fair? P (E'/J)?
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