Question

Stephanie's 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 Stephanie judges over a three-year period. Shown in Table below are the result for cases handled (disposed) by 4 judges in Ken's 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.

1. The probability of cases being appealed and reversed in the Ken's 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.

Ken's 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

(1) Prob. = (106+17)/30499 = 0.0040.

(2) Prob.(Penelope Cunningham) = 7/2729 = 0.0026
Prob.(Patrick Dinkelacker) = 19/6001 = 0.0032
Prob.(Deborah Gaines) = 48/8799 = 0.0055
Prob.(Ronald Panioto) = 32/12970 = 0.0025

(3) Prob.(Penelope Cunningham) = 1/2729 = 0.0004
Prob.(Patrick Dinkelacker) = 4/6001 = 0.0007
Prob.(Deborah Gaines) = 9/8799 = 0.0010
Prob.(Ronald Panioto) = 3/12970 = 0.0002

(4) Prob.(Penelope Cunningham) = 1/7 = 0.1429
Prob.(Patrick Dinkelacker) = 4/19 = 0.2105
Prob.(Deborah Gaines) = 9/48 = 0.1875
Prob.(Ronald Panioto) = 3/32 = 0.0938

(5) The judges would be ranked in the following order: Ronald Panioto, Penelope Cunningham, Patrick Dinkelacker, Deborah Gaines.
The judges have been ranked in increasing order of the probability of cases being appealed and reversed in the Ken's Court. This criteria has been used because this probability determines how much a particular judge has been accurate while providing a verdict, so that the least no. of appeals and reversals has taken place in his cases.