6.66 The authors of the paper “Do Physicians Know when Their Diagnoses Are Correct?” (Journal of Gen- eral 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 = event that diagnosis is correct

I = event that diagnosis is incorrect

H = 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:

P 1C 2 5 .261                P 1I 2 5 .739

P 1H 0 C 2 5 .375             P 1H 0 I 2 5 .073

Use Bayes’ rule to compute the probability of a cor- rect diagnosis given that the student’s confidence level in the correctness of the diagnosis is high.

 

Bold exercises answered in back                      Data set available online                    Video Solution available

 

374                 Chapter 6  Probability

 

 

 

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

P 1C 2 5 .495                P 1I 2 5 .505

P 1H 0 C 2 5 .537            P 1H 0 I 2 5 .252

Compute P 1C 0 H 2 for medical school faculty. How does the  value  of  this  probability  compare  to  the  value  of P 1C 0 H 2 for students computed in Part (a)?