6.67 The authors of the paper “Do Physicians Know when Their Diagnoses Are Correct?” (Journal of General Internal Medicine [2005]: 334–339) presented detailed case studies to medical students and to faculty at medical schools. Each participant was asked to provide a diagnosis in the case and also to indicate whether his or her confidence in the correctness of the diagnosis was high or low. Define the events C, I, and H as follows:

C 5 event that diagnosis is correct I 5 event that diagnosis is incorrect H 5 event that confidence in the correctness of the diagnosis is high

a. Data appearing in the paper were used to estimate the following probabilities for medical students:

PsCd 5 .261 PsI d 5 .739 PsHuCd 5 .375 PsHuI d 5 .073 Use Bayes’ rule to compute the probability of a correct diagnosis given that the student’s confidence level in the correctness of the diagnosis is high.

b. Data from the paper were also used to estimate the following probabilities for medical school faculty:

PsCd 5 .495 PsI d 5 .505 PsHuCd 5 .537 PsHuI d 5 .252 Compute PsCuHd for medical school faculty. How does the value of this probability compare to the value of PsCuHd for students computed in Part (a)?