Question

Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed, some of the cases are reversed. Kristen DelGuzzi of the Cincinnati Enquirer conducted a study of the cases handled by Hamilton County judges over a three-year period. Shown in Table below are the result for cases handled (disposed) by 4 judges in Domestic Relations Court. The purpose of the newspaper’s study was to evaluate the performance of the judges. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which judges were doing a good job and which were making too many mistakes. You have been called in to assist in the data analysis. Use your knowledge of probability and conditional probability to help with the ranking of the judges. Prepare a report with your rankings of the judges. Also, include an analysis of the likelihood of appeal and case reversal in the court. At a minimum, your report should include the following:

1. The probability of cases being appealed and reversed in the Domestic Relations Court.

2. The probability of a case being appealed for each judge.

3. The probability of a case being reversed for each judge

4. The probability of reversal given an appeal for each judge.

5. Rank the judges. State the criteria you used and provide a rationale for your choice.

PLEASE SHOW EXCEL FORMULAS

Domestic Relations Court
Judge	Total Cases Disposed	Appealed Cases	Reversed Case
Penelope Cunningham	2,729	7	1
Patrick Dinkelacker	6,001	19	4
Deborah Gaines	8,799	48	9
Ronald Panioto	12,970	32	3
Total	30,499	106	17

Answer 1

Judge	P(Appealed) = Appealed/Disposed	P(Reversed) = Reversed/Disposed	P(Reversed | Appealed) = Reversed/Appealed	Criteria for Ranking = P(Reversed | Appealed) / P(Appealed)
Penelope Cunningham	0.002565	0.000366	0.142857	55.69388
Patrick Dinkelacker	0.003166	0.000667	0.210526	66.49307
Deborah Gaines	0.005455	0.001023	0.1875	34.37109
Ronald Panioto	0.002467	0.000231	0.09375	37.99805
Total	0.003476	0.000557	0.160377

More the criteria of ranking, better the judge

Hence, Ranking: Patrick > Penelope > Ronald > Deborah