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 25% of the cases, Judge Brown saw 33% 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. 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(Judge brown) = 0.33

So,

P(Not Judge brown) = 1 - 0.33 = 0.67

P(Not appealed | Not Judge Brown)

= P(Not appealed and not judge brown)/ P(Not judge Brown)

= (0.25*0.96 + 0.42*0.91)/ 0.67

= 3111/3350

= 0.9287 [Rounded off to 4 decimal places]

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