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

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) = 0.262
P(HIC) = 0.344
P(I) = 0.738
P(H|I) = 0.074

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.)