In the JJ Judge Training School (??TS) we test whether judges can judges are hig
ID: 3368719 • Letter: I
Question
In the JJ Judge Training School (??TS) we test whether judges can judges are highly confident they have the correct result. Suppose the testers know if the defendants are guilty so we judges get the correct result. Let C be the event that the judge tell if the defendant is guilty or not and whether it matters if the gets the correct result. Let I be the event that the judge gets the wrong i.e. the complement of C. Let H be the event that the judge is highly confident in her/his choice. The following are the data from | the ))ITS, p(C) .495, p(HIC)-.572, p(HII)-.393. a. Calculate P(I) b. What proportion of the time are judges highly confident in their decision? c. What proportion of the time are judges both correct and highly confident in their decision? d. What proportion of the time are judges Correct given that they are highly confident. Add any comments below.Explanation / Answer
a)P(I)=1-P(C)=1-0.495=0.505
b)P(H)=P(I)*P(H|I)+P(C)*P(H|C)=0.505*0.393+0.495*0.572=0.481605
c)P(H and C)=P(C)*P(H|C) =0.495*0.572=0.28314
d)P(C|H)=P(H and C)/P(H)=0.28314/0.481605=0.587909