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.

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

• Table (b): Domestic Relations Court

Judge	P(Appealed Cases)	P(Reversed Cases)	P(Reversed | Appealed)	Rank
Penelope Cunningham	0.0026	0.0004	0.1429	3
Patrick Dinkelacker	0.0032	0.0007	0.2105	2
Deborah Gaines	0.0055	0.0010	0.1875	1
Ronald Panioto	0.0025	0.0002	0.0938	4
Total	0.0035	0.0006	0.1604

Probability of a case being appealed = number of cases appealed/ total number of cases disposed.

Probability of a case being reversed = number of cases reversed/ total number of cases disposed.

Probability of a case being reversed given they have been appealed = number of cases reversed/ number of cases appealed

The judge having lesser probability of a case being appealed/ reversed has been given a higher rank.