The authors of a paper 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(C) = 0.264
P(H|C) = 0.395
P(I) = 0.736
P(H|I) = 0.076
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. (Round your answer to three decimal places.)
(b)
Data from the paper were also used to estimate the following probabilities for medical school faculty.
P(C) = 0.495
P(H|C) = 0.571
P(I) = 0.505
P(H|I) = 0.257
Compute
P(C|H)
for medical school faculty. (Round your answer to three decimal places.)
How does the value of this probability compare to the value of
P(C|H)
for students computed in part (a)?
The result is a little higher for faculty than for students. A faculty member who has high confidence in a correct diagnosis is slightly more likely to actually be correct than a student who has the same high confidence.
The result is a little higher for faculty than for students. A faculty member who has high confidence in a correct diagnosis is slightly less likely to actually be correct than a student who has the same high confidence.
The result is a little lower for faculty than for students. A faculty member who has high confidence in a correct diagnosis is slightly less likely to actually be correct than a student who has the same high confidence.
The result is a little lower for faculty than for students. A faculty member who has high confidence in a correct diagnosis is slightly more likely to actually be correct than a student who has the same high confidence.