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 22% of the cases, Judge Brown saw 31% 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 8% of Judge Carter’s cases were appealed. (See the case problem on pages 221-223 of your textbook for a siv milar 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?

Explanation / Answer

P(not appealed | not Judge Brown) = P(not appealed and not Judge Brown) / P(not Judge Brown)

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

= 0.96*0.22 + 0.92*(1-0.22-0.31) = 0.6436

P(not Judge Brown) = 1 - 0.31 = 0.69

P(not appealed | not Judge Brown) = 0.6436 / 0.69 = 0.9328

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