Suppose you wanted to evaluate the performance of the three judges in Smallville

Question

Suppose you wanted to evaluate the performance of the three judges in Smallville, Texas: Judge Adams, Judge Brown, and Judge Carter. Over a three-year period in Smallville, Judge Adams saw 23% of the cases, Judge Brown saw 34% of the cases, and Judge Carter saw the remainder of the cases. 4% of Judge Adams’ cases were appealed, 6% of Judge Brown’s cases were appealed, and 9% of Judge Carter’s cases were appealed. (See the case problem on pages 221-223 of your textbook for a similar problem.) Given the judge in a case from this three-year period was not Judge Brown, what is the probability the case was not appealed? (answer must be typed to four decimals)

Explanation / Answer

probability that Judge Carter saw the case =1-0.23-0.34 =0.43

probability of  judge was not Judge Brown =1-0.34 =0.66

hence  probability the case was not appealed given  judge was not Judge Brown

=P(Judge Adams and not appealed+Judge Judge Carter and not appealed)/P(not Judge Brown)

=(0.23*(1-0.04)+0.43*(1-0.09))/0.66 =0.9274

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