Reporter Kristen DelGuzzi of The Cincinnati Enquirer is writing a piece about the effectiveness of judges in Hamilton County, Ohio. 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.

Over a three-year period the Hamilton County Common Pleas Court, Domestic Relations Court, and Municipal Court handled 182,908 cases. The purpose of the newspaper’s study is to evaluate the performance of each court and the judges who render their decisions. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which court and which judges were doing a good job and which were making too many mistakes.

You have been hired to assist in the data analysis at the court level (judge-level analysis will be done at a later time). You must use your knowledge of probability and conditional probability to help determine the likelihood of appeal and reversal for cases handled by different courts.

1) Out of all the appealed cases, what is the probability of a successful appeal?

a. 0.0551

b. 0.1351

c. 0.084

d. 0.1129

2) Which outcome has the highest probability of occurring based on the data?

a. A case in Domestic Relations Court being reversed

b.There is not enough information to determine the answer

c. A case in Common Pleas Court being reversed

3) What is the probability for any case being reversed?

A. 0.00453

B. 0.0017

C. 0.1129

 

TOTAL COURT CASES DISPOSED, APPEALED, AND REVERSED IN HAMILTON COUNTY COURTS, n = 182,908 Reversed n = 199 Appealed n = 1,762 Upheld n = 1,563 Common Pleas n = 43,945 Not Appealed n = 42,183 Reversed n = 17 Appealed n = 106 n = 182,908 Domestic Relations Upheld n = 89 n = 30,499 Not Appealed n = 30,393 Reversed n = 104 Appealed n = 500 Municipal Court n = 108,464 Upheld n = 396 Not Appealed n = 107,964 TOTAL COURT CASES DISPOSED, APPEALED, AND REVERSED IN HAMILTON COUNTY COURTS, n = 182,908 Reversed n = 199 Appealed n = 1,762 Upheld n = 1,563 Common Pleas n = 43,945 Not Appealed n = 42,183 Reversed n = 17 Appealed n = 106 n = 182,908 Domestic Relations Upheld n = 89 n = 30,499 Not Appealed n = 30,393 Reversed n = 104 Appealed n = 500 Municipal Court n = 108,464 Upheld n = 396 Not Appealed n = 107,964