Reporter Kristen DelGuzzi of The Cincinnati Enquirer is writing a piece about th

Question

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 199 na Appealed 1,762 Upheld Common Pleas 1,563 43,945 Not Appealed n 42,183 Reversed Appealed n 106 n 182,908 Domestic Relations Upheld n 30.499 89 Not Appealed 30,393 Reversed 104 Appealed 500 Municipal Court Upheld n 108,464 n 396 Not Appealed n 107,964

Explanation / Answer

1)

Out of 182908 appeals, 1563 + 89 + 396 = 2048 appeals are successfull. So the probability of a successful appeal is

2048 / 182908 = 0.0112

2)

Following option is correct:

c. A case in Common Pleas Court being reversed

3)

Number of cases reversed is 199+17+104 = 320

So the probability for any case being reversed is

320 / 182908 = 0.0017

Probability Common pleas 43945/182908 0.240257397 Domestic Relations 30499/182908 0.16674503 Municipal Court 108464/182908 0.592997573 Condition probabilites Appealed|Common pleas 1762/43945 0.040095574 Not Appealed|Common pleas 42183/43945 0.959904426 Appealed|Domestic relations 106/30499 0.003475524 Not Appealed|Domestic relations 30393/30499 0.996524476 Appealed|Municipal Court 500/108464 0.004609824 Not Appealed|Municipal Court 107964/108464 0.995390176 Reversed|Common pleas 199/43945 0.004528388 Upheld|Common pleas 1563/43945 0.035567186 Reversed|Domestic relations 17/30499 0.000557395 Upheld|Domestic relations 89/30499 0.002918128 Reversed|Municipal Court 104/108464 0.000958843 Upheld|Municipal Court 396/108464 0.003650981

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